• Order Pub Date : 2020-11-21
Anna Jenčová, Sylvia Pulmannová

Dimension effect algebras were introduced in Jenčová and Pulmannová (Rep. Math. Phys. 62, 205–218, 2008), and it was proved that they are unit intervals in dimension groups. We prove that the effect algebra tensor product of dimension effect algebras is a dimension effect algebra, which is the unit interval in the unital abelian po-groups tensor product of the corresponding dimension groups.

更新日期：2020-11-22
• Order Pub Date : 2020-11-20
Gábor Czédli, Robert C. Powers, Jeremy M. White

Let L be a lattice of finite length and let d denote the minimum path length metric on the covering graph of L. For any $$\xi =(x_{1},\dots ,x_{k})\in L^{k}$$, an element y belonging to L is called a median of ξ if the sum d(y,x1) + ⋯ + d(y,xk) is minimal. The lattice L satisfies the c1-median property if, for any $$\xi =(x_{1},\dots ,x_{k})\in L^{k}$$ and for any median y of ξ, $$y\leq x_{1}\vee \dots 更新日期：2020-11-21 • Order Pub Date : 2020-11-10 Jinbo Yang, Xiaoyong Xi Representing lattices by topologies has been studied to a great extent. In this paper, we prove that a complete lattice L is isomorphic to the lattice of open subsets of a P-space iff L is order generated by its countably prime elements. We establish the dual equivalence between the category of complete lattices order generated by their countably prime elements with morphisms preserving arbitrary sups 更新日期：2020-11-12 • Order Pub Date : 2020-11-09 Zhongyuan Che A perfect matching of a graph is a set of independent edges that covers all vertices of the graph. A bipartite graph is elementary if and only if it is connected and each edge is contained in a perfect matching. The resonance graph of a plane bipartite graph G is a graph whose vertices are perfect matchings of G, and two perfect matchings are adjacent if edges contained in their union but not intersection 更新日期：2020-11-09 • Order Pub Date : 2020-10-29 Heather C. Smith, William T. Trotter The original notion of dimension for posets was introduced by Dushnik and Miller in 1941 and has been studied extensively in the literature. In 1992, Brightwell and Scheinerman developed the notion of fractional dimension as the natural linear programming relaxation of the Dushnik-Miller concept. In 2016, Ueckerdt introduced the concept of local dimension, and in just three years, several research 更新日期：2020-10-30 • Order Pub Date : 2020-10-22 I. A. Bochkov, F. V. Petrov Let \((\mathcal {P},\leqslant )$$ be a finite poset. Define the numbers a1,a2,… (respectively, c1,c2,…) so that a1 + … + ak (respectively, c1 + … + ck) is the maximal number of elements of $$\mathcal {P}$$ which may be covered by k antichains (respectively, k chains.) Then the number $$e(\mathcal {P})$$ of linear extensions of poset $$\mathcal {P}$$ is not less than $$\prod a_{i}!$$ and not more than

更新日期：2020-10-30
• Order Pub Date : 2020-09-26
Bernd S. W. Schröder

Let $$\lambda \in \left (0,\frac {1}{2} \right )$$. We prove that, for ordered sets P of order dimension 2 and for interval orders, the ratio of the number of automorphisms to the number of endomorphisms is asymptotically bounded by $$2^{-|P|^{\lambda } }$$. The key to the proof is to establish this bound for certain types of lexicographic sums.

更新日期：2020-09-26
• Order Pub Date : 2020-09-24
Danica Jakubíková–Studenovská

A homomorphism quasi-order between algebraic structures $$\mathcal {A}$$ and $${\mathcal{B}}$$ of the same type is defined as follows: $${\mathscr{A}}\leq {\mathscr{B}}$$ if there is a homomorphism of $${\mathscr{A}}$$ to $${\mathscr{B}}$$. The paper deals with the class $${\mathcal{L}}$$ of all connected monounary algebras. Let $$\sim$$ be the equivalence corresponding to the relation ≤ and let $$\mathbb 更新日期：2020-09-24 • Order Pub Date : 2020-09-10 Hiroshi Hirai, So Nakashima A modular semilattice is a semilattice generalization of a modular lattice. We establish a Birkhoff-type representation theorem for modular semilattices, which says that every modular semilattice is isomorphic to the family of ideals in a certain poset with additional relations. This new poset structure, which we axiomatize in this paper, is called a PPIP (projective poset with inconsistent pairs) 更新日期：2020-09-10 • Order Pub Date : 2020-08-25 Wojciech Olszewski We generalize the famous Tarski result by showing that: if X is a complete lattice, and f : X → X is an order-preserving mapping, then for all points x ∈ X, the limit superior and the limit inferior of the (possibly transfinite) sequence of iterations x, f(x), f2(x)..., fβ(x),... are fixed points of f. These limits are the sharp fixed-point bounds between which sufficiently large transfinite iterations 更新日期：2020-08-25 • Order Pub Date : 2020-08-22 Liliana Alcón, Noemí Gudiño, Marisa Gutierrez A k-tree is either a complete graph on k vertices or a graph that contains a vertex whose neighborhood induces a complete graph on k vertices and whose removal results in a k-tree. If the comparability graph of a poset P is a k-tree, we say that P is a k-tree poset. In the present work, we study and characterize by forbidden subposets the k-tree posets that admit a containment model mapping vertices 更新日期：2020-08-22 • Order Pub Date : 2020-08-03 Mirko Navara, Pavel Pták Let \(\mathcal {S}$$ denote the class of orthomodular posets in which all maximal Frink ideals are selective. Let $$\mathcal {R}$$ (resp. HCode $$\mathcal {T}$$) be the class of orthomodular posets defined by the validity of the following implications: $$P\in \mathcal {R}$$ if the implication a,b ∈ P, $$a\wedge b=0\ \Rightarrow \ a\le b^{\prime }$$ holds (resp., $$P\in \mathcal {T}$$ if the implication

更新日期：2020-08-03
• Order Pub Date : 2020-07-29
Edward Kissin, Victor Shulman, Yuri Turovskii

We refine Amitsur’s theory of radicals in complete lattices and apply the obtained results to the theory of radicals in the lattices of subspaces of Banach spaces and in the lattices of ideals of Banach and C*-algebras and of Banach Lie algebras.

更新日期：2020-07-29
• Order Pub Date : 2020-07-23
Attila Sali, Gábor Simonyi, Gábor Tardos

In an earlier paper (see Sali and Simonyi Eur. J. Combin. 20, 93–99, 1999) the first two authors have shown that self-complementary graphs can always be oriented in such a way that the union of the oriented version and its isomorphically oriented complement gives a transitive tournament. We investigate the possibilities of generalizing this theorem to decompositions of the complete graph into three

更新日期：2020-07-23
• Order Pub Date : 2020-07-07
Efe A. Ok, Gil Riella

We say that a group is fully preorderable if every (left- and right-) translation invariant preorder on it can be extended to a translation invariant total preorder. Such groups arise naturally in applications, and relate closely to orderable and fully orderable groups (which were studied extensively since the seminal works of Philip Hall and A. I. Mal’cev in the 1950s). Our first main result provides

更新日期：2020-07-07
• Order Pub Date : 2020-06-27
A. G. Gein, M. P. Shushpanov

We prove the lattice freely generated by three distributive elements and the lattice freely generated by two distributive elements and one dually distributive element contain the free lattice of rank 3 as sublattice. We describe the lattice freely generated by two distributive elements and one both distributive and dually distributive element. It is infinite, but does not contain the free lattice of

更新日期：2020-06-27
• Order Pub Date : 2020-06-20
F. Ávila, G. Bezhanishvili, P. J. Morandi, A. Zaldívar

Let $$\mathcal {O} S$$ be the frame of open sets of a topological space S, and let $$N(\mathcal {O} S)$$ be the frame of nuclei on $$\mathcal {O} S$$. For an Alexandroff space S, we prove that $$N(\mathcal {O} S)$$ is spatial iff the infinite binary tree $${\mathscr{T}}_2$$ does not embed isomorphically into (S,≤), where ≤ is the specialization preorder of S.

更新日期：2020-06-22
• Order Pub Date : 2020-06-19
John Harding, Chris Heunen

Topos quantum mechanics, developed by Döring (2008); Döring and Harding Houston J. Math. 42(2), 559–568 (2016); Döring and Isham (2008); Flori 2013)); Flori (2018); Isham and Butterfield J. Theoret. Phys. 37, 2669–2733 (1998); Isham and Butterfield J. Theoret. Phys. 38, 827–859 (1999); Isham et al. J. Theoret. Phys. 39, 1413–1436 (2000); Isham and Butterfield J. Theoret. Phys. 41, 613–639 (2002), creates

更新日期：2020-06-19
• Order Pub Date : 2020-06-02
Csaba Biró, Bartłomiej Bosek, Heather C. Smith, William T. Trotter, Ruidong Wang, Stephen J. Young

Planar posets can have arbitrarily large dimension. However, a planar poset of height h has dimension at most 192h + 96, while a planar poset with t minimal elements has dimension at most 2t + 1. In particular, a planar poset with a unique minimal element has dimension at most 3. In this paper, we extend this result by showing that a planar poset has dimension at most 6 if it has a plane diagram in

更新日期：2020-06-02
• Order Pub Date : 2020-05-11
Noah Kravitz, Ashwin Sah

We address the following natural but hitherto unstudied question: what are the possible linear extension numbers of an n-element poset? Let LE(n) denote the set of all positive integers that arise as the number of linear extensions of some n-element poset. We show that LE(n) skews towards the “small” end of the interval [1, n!]. More specifically, LE(n) contains all of the positive integers up to $$\exp 更新日期：2020-05-11 • Order Pub Date : 2020-05-06 Mahir Bilen Can, Tien Le We continue our study of the inclusion posets of diagonal SL(n)-orbit closures in a product of two partial flag varieties. We prove that, if the diagonal action is of complexity one, then the poset is isomorphic to one of the 28 posets that we determine explicitly. Furthermore, our computations show that the number of diagonal SL(n)-orbits in any of these posets is at most 10 for any positive integer 更新日期：2020-05-06 • Order Pub Date : 2020-04-28 J. Pascal Gollin, Jakob Kneip Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets. First we characterise those tree sets that can be represented by tree sets arising from infinite trees; these are precisely those tree sets without a chain of order 更新日期：2020-04-28 • Order Pub Date : 2020-04-27 Martin Charles Golumbic, Vincent Limouzy We consider questions regarding the containment graphs of paths in a tree (CPT graphs), a subclass of comparability graphs, and the containment posets of paths in a tree (CPT orders). In 1984, Corneil and Golumbic observed that a graph G may be CPT, yet not every transitive orientation of G necessarily has a CPT representation, illustrating this on the even wheels W2k(k ≥ 3). Motivated by this example 更新日期：2020-04-27 • Order Pub Date : 2020-04-20 Jacob Menix, Tom Richmond If \(f:X \rightarrow X$$ is a function, the associated functional Alexandroff topology on X is the topology Pf whose closed sets are $$\{A \subseteq X : f(A) \subseteq A\}$$. We present a characterization of functional Alexandroff topologies on a finite set X and show that the collection FA(X) of all functional Alexandroff topologies on a finite set X, ordered by inclusion, is a complemented lattice

更新日期：2020-04-20
• Order Pub Date : 2020-03-26
Atrayee Majumder, Rogers Mathew, Deepak Rajendraprasad

A collection of linear orders on X, say $${\mathscr{L}}$$, is said to realize a partially ordered set (or poset) $$\mathcal {P} = (X, \preceq )$$ if, for any two distinct x,y ∈ X, x ≼ y if and only if x ≺Ly, $$\forall L \in {\mathscr{L}}$$. We call $${\mathscr{L}}$$ a realizer of $$\mathcal {P}$$. The dimension of $$\mathcal {P}$$, denoted by $$dim(\mathcal {P})$$, is the minimum cardinality of a realizer

更新日期：2020-03-26
• Order Pub Date : 2020-03-03
Jianning Su

Matoušek introduced and axiomatized a notion of symmetric difference for orthocomplemented lattices (OMLs) called the orthocomplemented difference lattics (ODLs). We focus on the class of all ODLs that are set-representable and prove that this class is not locally finite by constructing an infinite three-generated set-representable ODL. This result answers a question posed by Matoušek and Pták. We

更新日期：2020-03-03
• Order Pub Date : 2020-02-13
Giovanni Gaiffi, Viola Siconolfi

For any triple given by a positive integer n, a finite group G, and a faithful representation V of G, one can describe a subspace arrangement whose intersection lattice is a generalized Dowling lattice in the sense of Hanlon (Trans. Amer. Math. Soc. 325(1), 1–37, 1991). In this paper we construct the minimal De Concini-Procesi wonderful model associated to this subspace arrangement and give a description

更新日期：2020-02-13
• Order Pub Date : 2020-02-13
Jean-Philippe Labbé, Carsten E. M. C. Lange

We study the size of certain acyclic domains that arise from geometric and combinatorial constructions. These acyclic domains consist of all permutations visited by commuting equivalence classes of maximal reduced decompositions if we consider the symmetric group and, more generally, of all c-singletons of a Cambrian lattice associated to the weak order of a finite Coxeter group. For this reason, we

更新日期：2020-02-13
• Order Pub Date : 2020-02-10
Dániel Gerbner; Balázs Keszegh; Balázs Patkós

A subfamily $$\{F_{1},F_{2},\dots ,F_{|P|}\}\subseteq \mathcal {F}$$ of sets is a copy of a poset P in $$\mathcal {F}$$ if there exists a bijection $$\phi :P\rightarrow \{F_{1},F_{2},\dots ,F_{|P|}\}$$ such that whenever $$x \le _{P} x^{\prime }$$ holds, then so does $$\phi (x)\subseteq \phi (x^{\prime })$$. For a family $$\mathcal {F}$$ of sets, let $$c(P,\mathcal {F})$$ denote the number of copies

更新日期：2020-02-10
• Order Pub Date : 2020-01-22
Claudia Mureşan, Júlia Kulin

We investigate the possible values of the numbers of congruences of finite lattices of an arbitrary but fixed cardinality. Motivated by a result of Freese and continuing Czédli’s recent work, we prove that the third, fourth and fifth largest numbers of congruences of an n–element lattice are: 5 ⋅ 2n− 5 if n ≥ 5, 2n− 3 and 7 ⋅ 2n− 6 if n ≥ 6, respectively. We also determine the structures of the n–element

更新日期：2020-01-22
• Order Pub Date : 2020-01-10
M. E. Adams, H. P. Sankappanavar, Júlia Vaz de Carvalho

In this paper, we investigate the varieties Mn and Kn of regular pseudocomplemented de Morgan and Kleene algebras of range n, respectively. Priestley duality as it applies to pseudocomplemented de Morgan algebras is used. We characterise the dual spaces of the simple (equivalently, subdirectly irreducible) algebras in Mn and explicitly describe the dual spaces of the simple algebras in M1 and K1. We

更新日期：2020-01-10
• Order Pub Date : 2019-12-27
Masato Kobayashi

We generalize the author’s formula (2011) on weighted counting of inversions on permutations to one on alternating sign matrices. The proof is based on the sequential construction of alternating sign matrices from the unit matrix which essentially follows from the earlier work of Lascoux-Schützenberger (1996).

更新日期：2019-12-27
• Order Pub Date : 2019-12-18
Gábor Czédli

Let L be a finite n-element semilattice. We prove that if L has at least 127 ⋅ 2n− 8 subsemilattices, then L is planar. For n > 8, this result is sharp since there is a non-planar semilattice with exactly 127 ⋅ 2n− 8 − 1 subsemilattices.

更新日期：2019-12-18
• Order Pub Date : 2019-12-13
Themba Dube

We say a prime element of an algebraic frame is amenable if it comparable to every compact element. If every prime element of an algebraic frame L is amenable, we say L is an amenable frame. If the localization of L at every prime element is amenable, we say L is locally amenable. These concepts are motivated by notions of divided and locally divided commutative rings. We show that an algebraic frame

更新日期：2019-12-13
• Order Pub Date : 2019-12-09
Reinhard Diestel; Jakob Kneip

Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory about infinite separation systems and how they relate to the finite separation systems they induce. They can be used to prove tangle-type duality theorems for infinite

更新日期：2019-12-09
• Order Pub Date : 2019-11-22
Joshua Cooper; Peter Gartland; Hays Whitlatch

Hasebe and Tsujie characterized the set of induced N-free and bowtie-free posets as a certain class of recursively defined subposets which they term “$$\mathcal {V}$$-posets”. Here we offer a new characterization of $$\mathcal {V}$$-posets by introducing a property we refer to as autonomy. A poset $$\mathcal {P}$$ is said to be autonomous if there exists a directed acyclic graph D (with adjacency matrix

更新日期：2019-11-22
• Order Pub Date : 2019-11-19
Nathan Bowler; Jakob Kneip

Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as separation systems of graphs, sets, or set bipartitions.

更新日期：2019-11-19
• Order Pub Date : 2019-11-19
D. Georgiou, S. Iliadis, A. Megaritis, F. Sereti

The universality property plays an important role in the field of frames and the notion of saturated class of frames is combined with this property (see Dube et al. (Topology and its Applications 160, 2454–2464, 2013); Iliadis (Topology and its Applications 179, 99–110, 2015) and Iliadis (Topology and its Applications 201, 92–109, 18)). In this paper, we continue such a study, introducing and studying

更新日期：2019-11-19
• Order Pub Date : 2019-11-16

For a finite subset M ⊂ [x1,…, xd] of monomials, we describe how to constructively obtain a monomial ideal $$I\subseteq R = K[x_{1},\ldots ,x_{d}]$$ such that the set of monomials in Soc(I) ∖ I is precisely M, or such that $$\overline {M}\subseteq R/I$$ is a K-basis for the the socle of R/I. For a given M we obtain a natural class of monomials ideals I with this property. This is done by using solely

更新日期：2019-11-16
• Order Pub Date : 2019-11-07
Oleh Nykyforchyn; Oksana Mykytsey

Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their ambiguous representations, for which taking pseudo-inverse is involutive, form categories. Self-dualities and contravariant equivalences for these categories are obtained

更新日期：2019-11-07
• Order Pub Date : 2019-10-22
Seyed Hadi Afzali Borujeni; Nathan Bowler

By considering the number of maximal chains going through each element of an arbitrary poset, we prove an extension of Erdős’s generalisation of Sperner’s Theorem, together with a partial converse. By considering the number of maximal chains between pairs of comparable elements, we also prove a generalisation of the LYM inequality.

更新日期：2019-10-22
• Order Pub Date : 2019-09-21
Christian Gaetz; Praveen Venkataramana

We study the gaps Δpn between consecutive rank sizes in r-differential posets by introducing a projection operator whose matrix entries can be expressed in terms of the number of certain paths in the Hasse diagram. We strengthen Miller’s result that Δpn ≥ 1, which resolved a longstanding conjecture of Stanley, by showing that Δpn ≥ 2r. We also obtain stronger bounds in the case that the poset has many

更新日期：2019-09-21
• Order Pub Date : 2019-09-14
Tamás Mészáros; Piotr Micek; William T. Trotter

We investigate the behavior of Boolean dimension with respect to components and blocks. To put our results in context, we note that for Dushnik-Miller dimension, we have that if $$\dim (C)\le d$$ for every component C of a poset P, then $$\dim (P)\le \max \limits \{2,d\}$$; also if $$\dim (B)\le d$$ for every block B of a poset P, then $$\dim (P)\le d+2$$. By way of constrast, local dimension is well

更新日期：2019-09-14
• Order Pub Date : 2019-09-04
Yibo Gao

Valuations on finite lattices have been known for a long time. In this paper, we present a combinatorial procedure called modularization that associates a modular lattice to any given finite lattice such that they have the same valuation polytopes.

更新日期：2019-09-04
• Order Pub Date : 2019-08-16
Fidel Barrera-Cruz; Thomas Prag; Heather C. Smith; Libby Taylor; William T. Trotter

The original notion of dimension for posets is due to Dushnik and Miller and has been studied extensively in the literature. Quite recently, there has been considerable interest in two variations of dimension known as Boolean dimension and local dimension. For a poset P, the Boolean dimension of P and the local dimension of P are both bounded from above by the dimension of P and can be considerably

更新日期：2019-08-16
• Order Pub Date : 2019-08-03
Sergey V. Gusev; Hanamantagouda P. Sankappanavar; Boris M. Vernikov

An implication semigroup is an algebra of type (2, 0) with a binary operation → and a 0-ary operation 0 satisfying the identities $$(x\rightarrow y)\rightarrow z\approx x\rightarrow (y\rightarrow z)$$, $$(x\rightarrow y)\rightarrow z\approx \left [(z^{\prime }\rightarrow x)\rightarrow (y\rightarrow z)'\right ]'$$ and $$0^{\prime \prime }\approx 0$$ where $$\mathbf {u}^{\prime }$$ means $$\mathbf u\rightarrow 更新日期：2019-08-03 • Order Pub Date : 2019-07-24 Shahriar Shahriari; Song Yu Let n be a positive integer, q a power of a prime, and \(\mathcal {L}_{n}({q})$$ the poset of subspaces of an n-dimensional vector space over a field with q elements. This poset is a normalized matching poset and the set of subspaces of dimension ⌊n/2⌋ or those of dimension ⌈n/2⌉ are the only maximum-sized antichains in this poset. Strengthening this well-known and celebrated result, we show that,

更新日期：2019-07-24
• Order Pub Date : 2019-07-20
Gergő Gyenizse

In this paper, we investigate the class of lattices representable with posets satisfying the DCC condition. We describe a way to decide whether a finite lattice is in this class. We also give a necessary condition for an arbitrary lattice to be in this class. This hints at a notion that would be a weaker version of lower boundedness.

更新日期：2019-07-20
• Order Pub Date : 2019-06-26
Miloš S. Kurilić; Stevo Todorčević

We show that the poset of copies $$\mathbb {P} (\mathbb {Q}_{n} )=\langle \{ f[X]: f\in \text {Emb} (\mathbb {Q}_{n} ) \},\subset \rangle$$ of the countable homogeneous universal n-labeled linear order, $$\mathbb {Q}_{n}$$, is forcing equivalent to the poset $$\mathbb {S} \ast \pi$$, where $$\mathbb {S}$$ is the Sacks perfect set forcing and $$1_{\mathbb {S}} \Vdash  \pi$$ is an atomless separative

更新日期：2019-06-26
• Order Pub Date : 2019-06-19
Rosário Fernandes; Henrique F. da Cruz; Domingos Salomão

Given two nonincreasing integral vectors R and S, with the same sum, we denote by $$\mathcal {A}(R,S)$$ the class of all (0,1)-matrices with row sum vector R, and column sum vector S. The Bruhat order and the Secondary Bruhat order on $$\mathcal {A}(R,S)$$ are both extensions of the classical Bruhat order on Sn, the symmetric group of degree n. These two partial orders on $$\mathcal {A}(R,S)$$ are

更新日期：2019-06-19
• Order Pub Date : 2019-06-10
Bernd S. W. Schröder

We prove that, for a finite ordered set P that contains no crowns with 6 or more elements, it can be determined in polynomial time if P has the fixed point property. This result is obtained by proving that every such ordered set must contain a point of rank 1 that has a unique lower cover or a retractable minimal element.

更新日期：2019-06-10
• Order Pub Date : 2019-06-10
Johannes Marti; Riccardo Pinosio

In this paper we present a duality between nonmonotonic consequence relations and well-founded convex geometries. On one side of the duality we consider nonmonotonic consequence relations satisfying the axioms of an infinitary variant of System P, which is one of the most studied axiomatic systems for nonmonotonic reasoning, conditional logic and belief revision. On the other side of the duality we

更新日期：2019-06-10
• Order Pub Date : 2019-06-10
Henri Mühle; Vivien Ripoll

We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of an element in a generated group. While one form of connectivity essentially reflects the connectivity of the poset diagram, the other two are a bit more involved: Hurwitz-connectivity has its origins in algebraic geometry, and shellability in topology. We propose a framework

更新日期：2019-06-10
• Order Pub Date : 2019-06-07

A poset $$\mathbb {P}$$ is called reversible iff every bijective homomorphism $$f:\mathbb {P} \rightarrow \mathbb {P}$$ is an automorphism. Let $$\mathcal {W}$$ and $$\mathcal {W}^{*}$$ denote the classes of well orders and their inverses respectively. We characterize reversibility in the class of posets of the form $$\mathbb {P} =\bigcup _{i\in I}\mathbb {L}_{i}$$, where $$\mathbb {L}_{i}, i\in I$$

更新日期：2019-06-07
• Order Pub Date : 2019-05-25
Wenfeng Zhang; Xiaoquan Xu

Given any subset selection $$\mathcal {Z}$$ for posets, we study two weakenings of the known concept of $$\mathcal {Z}$$-predistributivity, namely, $$\mathcal {Z}$$-quasidistributivity and $$\mathcal {Z}$$-meet-distributivity. The former generalizes quasicontinuity, and the latter meet-continuity of complete lattices. We show for global completions $$\mathcal {Z}$$ that the $$\mathcal {Z}$$-quasidistributive

更新日期：2019-05-25
• Order Pub Date : 2019-05-23
Noga Alon; Omri Ben-Eliezer

It was recently proved in Alon et al. (2017) that any hereditary property of two-dimensional matrices (where the row and column order is not ignored) over a finite alphabet is testable with a constant number of queries, by establishing the following ordered matrix removal lemma: For any finite alphabet Γ, any hereditary property $$\mathcal {P}$$ of matrices over Γ, and any 𝜖 > 0, there exists \(f_{\mathcal

更新日期：2019-05-23
• Order Pub Date : 2019-05-10
Ádám Kunos,Miklós Maróti,László Zádori

The article On Finite Generability of Clones of Finite Posets, written by Ádám Kunos, Miklós Maróti, and László Zádori was originally published electronically on the publisher’s internet portal (currently SpringerLink) on April 04, 2019 without open access.

更新日期：2019-05-10
• Order Pub Date : 2019-05-04
Jimmy Devillet; Bruno Teheux

We characterize the associative, idempotent, symmetric, and order-preserving binary operations on (finite) chains in terms of properties of (the Hasse diagram of) their associated semilattice order. In particular, we prove that the number of associative, idempotent, symmetric, and order-preserving operations on an n-element chain is the nth Catalan number.

更新日期：2019-05-04
• Order Pub Date : 2019-05-01
Ivan Chajda; Helmut Länger; Jan Paseka

In Chajda and Länger (Math. Bohem. 143, 89–97, 2018) the concept of relative pseudocomplementation was extended to posets. We introduce the concept of a congruence in a relatively pseudocomplemented poset within the framework of Hilbert algebras and we study under which conditions the quotient structure is a relatively pseudocomplemented poset again. This problem is solved e.g. for finite or linearly

更新日期：2019-05-01
• Order Pub Date : 2019-04-08
Taewon Yang

Let L and M be zero-dimensional frames. It is shown that concerning the Banaschewski compactification ζ, a necessary and sufficient condition for the canonically induced frame homomorphism hL,M : ζL ⊕ ζM→ζ(L ⊕ M) to be an isomorphism is given in terms of the tensor product of the rings of all bounded integer-valued continuous functions on L and M, respectively. This provides the integral counterpart

更新日期：2019-04-08
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