当前期刊: Order Go to current issue    加入关注   
显示样式:        排序: IF: - GO 导出
我的关注
我的收藏
您暂时未登录!
登录
  • Planar Posets that are Accessible from Below Have Dimension at Most 6
    Order (IF 0.424) 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
  • Linear Extension Numbers of n -Element Posets
    Order (IF 0.424) 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
  • Diagonal Orbits in a Type A Double Flag Variety of Complexity One
    Order (IF 0.424) 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
  • Representations of Infinite Tree Sets
    Order (IF 0.424) 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
  • Containment Graphs and Posets of Paths in a Tree: Wheels and Partial Wheels
    Order (IF 0.424) 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
  • The Lattice of Functional Alexandroff Topologies
    Order (IF 0.424) 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
  • Dimension of CPT Posets
    Order (IF 0.424) 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
  • On Set-Representable Orthocomplemented Difference Lattices
    Order (IF 0.424) 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
  • Wonderful Models for Generalized Dowling Arrangements
    Order (IF 0.424) 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
  • Cambrian Acyclic Domains: Counting c -singletons
    Order (IF 0.424) 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
  • Generalized Forbidden Subposet Problems
    Order (IF 0.424) 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
  • On the Largest Numbers of Congruences of Finite Lattices
    Order (IF 0.424) 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
  • Varieties of Regular Pseudocomplemented de Morgan Algebras
    Order (IF 0.424) 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
  • Weighted Counting of Inversions on Alternating Sign Matrices
    Order (IF 0.424) 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
  • One Hundred Twenty-Seven Subsemilattices and Planarity
    Order (IF 0.424) 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
  • Amenable and Locally Amenable Algebraic Frames
    Order (IF 0.424) 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
  • Profinite Separation Systems
    Order (IF 0.424) 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
  • A New Characterization of V$\mathcal {V}$ -Posets
    Order (IF 0.424) 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
  • Separations of Sets
    Order (IF 0.424) 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
  • Universality Property and Dimension for Frames
    Order (IF 0.424) 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
  • On Monomial Ideals and Their Socles
    Order (IF 0.424) Pub Date : 2019-11-16
    Geir Agnarsson, Neil Epstein

    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
  • On Lattice Representations with Dcc Posets
    Order (IF 0.424) 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
  • Posets of Copies of Countable Non-Scattered Labeled Linear Orders
    Order (IF 0.424) 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
  • Fixed Point Property for Finite Ordered Sets that Contain No Crowns with 6 or More Elements
    Order (IF 0.424) 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
  • A Discrete Duality Between Nonmonotonic Consequence Relations and Convex Geometries
    Order (IF 0.424) 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
  • Connectivity Properties of Factorization Posets in Generated Groups
    Order (IF 0.424) 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
  • Reversible Disjoint Unions of Well Orders and Their Inverses
    Order (IF 0.424) Pub Date : 2019-06-07
    Miloš S. Kurilić, Nenad Morača

    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
  • Z$\mathcal {Z}$ -quasidistributive and Z$\mathcal {Z}$ -meet-distributive Posets
    Order (IF 0.424) 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
  • Efficient Removal Lemmas for Matrices
    Order (IF 0.424) 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
  • Associative, Idempotent, Symmetric, and Order-preserving Operations on Chains
    Order (IF 0.424) 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
  • Algebraic Aspects of Relatively Pseudocomplemented Posets
    Order (IF 0.424) 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
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
如何通过Nature平台传播科研成果
跟Nature、Science文章学绘图
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
中洪博元
ACS材料视界
x-mol收录
南开大学
朱守非
廖良生
郭东升
西湖大学
伊利诺伊大学香槟分校
徐明华
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug