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Bi-primitive 2-arc-transitive bi-Cayley graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2024-03-02 Jing Jian Li, Xiao Qian Zhang, Jin-Xin Zhou
A bipartite graph \(\Gamma \) is a bi-Cayley graph over a group H if \(H\leqslant \textrm{Aut}\Gamma \) acts regularly on each part of \(\Gamma \). A bi-Cayley graph \(\Gamma \) is said to be a normal bi-Cayley graph over H if \(H\unlhd \textrm{Aut}\Gamma \), and bi-primitive if the bipartition preserving subgroup of \(\textrm{Aut}\Gamma \) acts primitively on each part of \(\Gamma \). In this paper
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On regular sets in Cayley graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2024-03-02 Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou
Let \(\Gamma = (V, E)\) be a graph and a, b nonnegative integers. An (a, b)-regular set in \(\Gamma \) is a nonempty proper subset D of V such that every vertex in D has exactly a neighbours in D and every vertex in \(V{\setminus }D\) has exactly b neighbours in D. A (0, 1)-regular set is called a perfect code, an efficient dominating set, or an independent perfect dominating set. A subset D of a group
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Power graphs of a class of completely 0-simple semigroups J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-26 Yanliang Cheng, Yong Shao, Lingli Zeng
We first determine the structure of the power digraphs of completely 0-simple semigroups, and then some properties of their power graphs are given. As the main result in this paper, using Cameron and Ghosh’s theorem about power graphs of abelian groups, we obtain a characterization that two \(G^{0}\)-normal completely 0-simple orthodox semigroups S and T with abelian group \(\mathcal {H}\)-classes
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Anti-dendriform algebras, new splitting of operations and Novikov-type algebras J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-26
Abstract We introduce the notion of an anti-dendriform algebra as a new approach of splitting the associativity. It is characterized as the algebra with two multiplications giving their left and right multiplication operators, respectively, such that the opposites of these operators define a bimodule structure on the sum of these two multiplications, which is associative. This justifies the terminology
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Alternating groups as products of cycle classes - II J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-26 Harish Kishnani, Rijubrata Kundu, Sumit Chandra Mishra
Given integers \(k,l\ge 2\), where either l is odd or k is even, let n(k, l) denote the largest integer n such that each element of \(A_n\) is a product of k many l-cycles. M. Herzog, G. Kaplan and A. Lev conjectured that \(\lfloor \frac{2kl}{3} \rfloor \le n(k,l)\le \lfloor \frac{2kl}{3}\rfloor +1\) [Herzog et al. in J Combin Theory Ser A, 115:1235-1245 2008]. It is known that the conjecture holds
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Multi-part cross-intersecting families J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-25 Yuanxiao Xi, Xiangliang Kong, Gennian Ge
Let \({\mathcal {A}}\subseteq {[n]\atopwithdelims ()a}\) and \({\mathcal {B}}\subseteq {[n]\atopwithdelims ()b}\) be two families of subsets of [n], we say \({\mathcal {A}}\) and \({\mathcal {B}}\) are cross-intersecting if \(A\cap B\ne \emptyset \) for all \(A\in {\mathcal {A}}\), \(B\in {\mathcal {B}}\). In this paper, we study cross-intersecting families in the multi-part setting. By characterizing
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Resistance diameters and critical probabilities of Cayley graphs on irreducible complex reflection groups J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-25 Maksim Vaskouski, Hanna Zadarazhniuk
We consider networks on minimal Cayley graphs of irreducible complex reflection groups G(m, p, n). We show that resistance diameters of these graphs have asymptotic \(\Theta (1/n)\) as \(n\rightarrow \infty \) under fixed m, p. Non-trivial lower and upper asymptotic bounds for critical probabilities of percolation for there appearing a giant connected component have been obtained.
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Common transversals and complements in abelian groups J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-24
Abstract Given a finite abelian group G and cyclic subgroups A, B, C of G of the same order, we find necessary and sufficient conditions for A, B, C to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete
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A note on “Largest independent sets of certain regular subgraphs of the derangement graph” J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-23 Yuval Filmus, Nathan Lindzey
Let \(D_{n,k}\) be the set of all permutations of the symmetric group \(S_n\) that have no cycles of length i for all \(1 \le i \le k\). In the paper mentioned above, Ku, Lau, and Wong prove that the set of all the largest independent sets of the Cayley graph \(\text {Cay}(S_n,D_{n,k})\) is equal to the set of all the largest independent sets in the derangement graph \(\text {Cay}(S_n,D_{n,1})\), provided
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Using mixed dihedral groups to construct normal Cayley graphs and a new bipartite 2-arc-transitive graph which is not a Cayley graph J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-23 Daniel R. Hawtin, Cheryl E. Praeger, Jin-Xin Zhou
A mixed dihedral group is a group H with two disjoint subgroups X and Y, each elementary abelian of order \(2^n\), such that H is generated by \(X\cup Y\), and \(H/H'\cong X\times Y\). In this paper, we give a sufficient condition such that the automorphism group of the Cayley graph \(\textrm{Cay}(H,(X\cup Y){\setminus }\{1\})\) is equal to \(H\rtimes A(H,X,Y)\), where A(H, X, Y) is the setwise stabiliser
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Compact hyperbolic Coxeter four-dimensional polytopes with eight facets J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-20 Jiming Ma, Fangting Zheng
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The direct sum of q-matroids J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-17 Michela Ceria, Relinde Jurrius
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A rank augmentation theorem for rank three string C-group representations of the symmetric groups J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-16 Julie De Saedeleer, Dimitri Leemans, Jessica Mulpas
We give a rank augmentation technique for rank three string C-group representations of the symmetric group \(S_n\) and list the hypotheses under which it yields a valid string C-group representation of rank four thereof.
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Basis condition for generalized spline modules J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-15 Seher Fişekci, Samet Sarıoğlan
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Finite Young wall model for representations of $$\imath $$ quantum group $${\textbf{U}}^{\jmath }$$ J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-08 Shaolong Han
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The Canonical component of the nilfibre for parabolic adjoint action in type A J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-07
Abstract This work is a continuation of [Y. Fittouhi and A. Joseph, Parabolic adjoint action, Weierstrass Sections and components of the nilfibre in type A]. Let P be a parabolic subgroup of an irreducible simple algebraic group G. Let \(P'\) be the derived group of P, and let \({\mathfrak {m}}\) be the Lie algebra of the nilradical of P. A theorem of Richardson implies that the subalgebra \({\mathbb
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Chain algebras of finite distributive lattices J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-06 Oleksandra Gasanova, Lisa Nicklasson
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Weight bounds for $$(3,\gamma )$$ -hyperelliptic curves J. Algebraic Comb. (IF 0.8) Pub Date : 2024-02-05
Abstract \((N,\gamma )\) -hyperelliptic semigroups were introduced by Fernando Torres to encapsulate the most salient properties of Weierstrass semigroups associated with totally ramified points of N-fold covers of curves of genus \(\gamma \) . Torres characterized \((2,\gamma )\) -hyperelliptic semigroups of maximal weight whenever their genus is large relative to \(\gamma \) . Here we do the same
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Beyond symmetry in generalized Petersen graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2024-01-24 Ignacio García-Marco, Kolja Knauer
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Maximum degree and spectral radius of graphs in terms of size J. Algebraic Comb. (IF 0.8) Pub Date : 2024-01-20 Zhiwen Wang, Ji-Ming Guo
Denote by \(\rho (G)\) and \(\kappa (G)\) the spectral radius and the signless Laplacian spectral radius of a graph G, respectively. Let \(k\ge 0\) be a fixed integer and G be a graph of size m which is large enough. We show that if \(\rho (G)\ge \sqrt{m-k}\), then \(C_4\subseteq G\) or \(K_{1,m-k}\subseteq G\). Moreover, we prove that if \(\kappa (G)\ge m-k+1\), then \(K_{1,m-k}\subseteq G\). Both
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Perfect state transfer on quasi-abelian semi-Cayley graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2024-01-20 Shixin Wang, Majid Arezoomand, Tao Feng
Perfect state transfer on graphs has attracted extensive attention due to its application in quantum information and quantum computation. A graph is a semi-Cayley graph over a group G if it admits G as a semiregular subgroup of the full automorphism group with two orbits of equal size. A semi-Cayley graph SC(G, R, L, S) is called quasi-abelian if each of R, L and S is a union of some conjugacy classes
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Cactus groups, twin groups, and right-angled Artin groups J. Algebraic Comb. (IF 0.8) Pub Date : 2024-01-10 Paolo Bellingeri, Hugo Chemin, Victoria Lebed
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Quivers and path semigroups characterized by locality conditions J. Algebraic Comb. (IF 0.8) Pub Date : 2023-12-28 Shanghua Zheng, Li Guo
Path algebras from quivers are a fundamental class of algebras with wide applications. Yet it is challenging to describe their universal properties since their underlying path semigroups are only partially defined. A new notion, called locality structures, was recently introduced to deal with partially defined operation, with motivation from locality in convex geometry and quantum field theory. We
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Riemann–Hurwitz theorem and Riemann–Roch theorem for hypermaps J. Algebraic Comb. (IF 0.8) Pub Date : 2023-12-26 Mengnan Cheng, Tingbin Cao
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On edge-transitive metacyclic covers of cubic arc-transitive graphs of order twice a prime J. Algebraic Comb. (IF 0.8) Pub Date : 2023-12-26 Xue Wang, Jin-Xin Zhou, Jaeun Lee
Let p be a prime, and let \(\Lambda _{2p}\) be a connected cubic arc-transitive graph of order 2p. In the literature, a lot of works have been done on the classification of edge-transitive normal covers of \(\Lambda _{2p}\) for specific \(p\le 7\). An interesting problem is to generalize these results to an arbitrary prime p. In 2014, Zhou and Feng classified edge-transitive cyclic or dihedral normal
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Asymptotic regularity of invariant chains of edge ideals J. Algebraic Comb. (IF 0.8) Pub Date : 2023-12-21 Do Trong Hoang, Hop D. Nguyen, Quang Hoa Tran
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Decreasing behavior of the depth functions of edge ideals J. Algebraic Comb. (IF 0.8) Pub Date : 2023-11-23 Ha Thi Thu Hien, Ha Minh Lam, Ngo Viet Trung
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On the automorphism groups of regular maps J. Algebraic Comb. (IF 0.8) Pub Date : 2023-11-23 Xiaogang Li, Yao Tian
Let \(\mathcal{M}\) be an orientably regular (resp. regular) map with the number n vertices. By \(G^+\) (resp. G) we denote the group of all orientation-preserving automorphisms (resp. all automorphisms) of \(\mathcal{M}\). Let \(\pi \) be the set of prime divisors of n. A Hall \(\pi \)-subgroup of \(G^+\)(resp. G) is meant a subgroup such that the prime divisors of its order all lie in \(\pi \) and
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An example of a non-associative Moufang loop of point classes on a cubic surface J. Algebraic Comb. (IF 0.8) Pub Date : 2023-11-08 D. Kanevsky
Let V be a cubic surface defined by the equation \(T_0^3+T_1^3+T_2^3+\theta T_3^3=0\) over a quadratic extension of 3-adic numbers \(k=\mathbb {Q}_3(\theta )\), where \(\theta ^3=1\). We show that a relation on a set of geometric k-points on V modulo \((1-\theta )^3\) (in a ring of integers of k) defines an admissible relation and a commutative Moufang loop associated with classes of this admissible
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On the socle of Artinian algebras associated with graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2023-11-02 Jorge Neves
Given a simple graph, consider the polynomial ring with coefficients in a field and variables identified with the edges of the graph. Given a non-empty even cardinality Eulerian subgraph and a choice of half of its edges, consider the homogeneous binomial obtained by taking the product of these edges minus the product of the remaining edges of the subgraph. We define a homogeneous ideal by taking as
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Constructions and equivalence of Sidon spaces J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-24 Chiara Castello, Olga Polverino, Paolo Santonastaso, Ferdinando Zullo
Sidon spaces have been introduced by Bachoc et al. (in: Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 2017) as the q-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth et al. (IEEE Trans Inform Theory 64(6):4412–4422, 2017), in which they highlighted the correspondence between Sidon spaces and
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Calabi–Yau operators of degree two J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-10 Gert Almkvist, Duco van Straten
We show that the solutions to the equations, defining the so-called Calabi–Yau condition for fourth-order operators of degree two, define a variety that consists of ten irreducible components. These can be described completely in parametric form, but only two of the components seem to admit arithmetically interesting operators. We include a description of the 69 essentially distinct fourth-order Calabi–Yau
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The popularity gap J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-04 Vsevolod F. Lev, Ilya D. Shkredov
Suppose that A is a finite, nonempty subset of a cyclic group of either infinite or prime order. We show that if the difference set \(A-A\) is “not too large”, then there is a nonzero group element with at least as many as \((2+o(1))|A|^2/|A-A|\) representations as a difference of two elements of A; that is, the second largest number of representations is, essentially, twice the average. Here the coefficient
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Edge ideals of Erdős–Rényi random graphs: linear resolution, unmixedness and regularity J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-05 Arindam Banerjee, D. Yogeshwaran
We study the homological algebra of edge ideals of Erdős–Rényi random graphs. These random graphs are generated by deleting edges of a complete graph on n vertices independently of each other with probability \(1-p\). We focus on some aspects of these random edge ideals—linear resolution, unmixedness and algebraic invariants like the Castelnuovo–Mumford regularity, projective dimension and depth. We
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On Schur rings over infinite groups III J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-05 Nicholas Bastian, Andrew Misseldine
In the paper, we develop further the properties of Schur rings over infinite groups, with particular emphasis on the virtually cyclic group \(\mathcal {Z}\times \mathcal {Z}_p\), where p is a prime. We provide structure theorems for primitive sets in these Schur rings. In the case of Fermat and safe primes, a complete classification theorem is proven, which states that all Schur rings over \(\mathcal
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Hexavalent edge-transitive graphs of order $$3p^2$$ J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-04 Song-Tao Guo, Li Wang
A graph is edge-transitive if its automorphism group acts transitively on the set of edges of the graph. In this paper, we classify hexavalent edge-transitive graphs of order \(3p^2\) for each prime p.
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On groups with chordal power graph, including a classification in the case of finite simple groups J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-04 Jendrik Brachter, Eda Kaja
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On basic 2-arc-transitive graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-04 Zai Ping Lu, Ruo Yu Song
A connected graph \(\Gamma =(V,E)\) of valency at least 3 is called a basic 2-arc-transitive graph if its full automorphism group has a subgroup G with the following properties: (i) G acts transitively on the set of 2-arcs of \(\Gamma \), and (ii) every minimal normal subgroup of G has at most two orbits on V. Based on Praeger’s theorems on 2-arc-transitive graphs, this paper presents a further understanding
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Quantum state transfer between twins in weighted graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2023-10-03 Steve Kirkland, Hermie Monterde, Sarah Plosker
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Cutoff phenomenon for the warp-transpose top with random shuffle J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-29 Subhajit Ghosh
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Characterisation of all integral circulant graphs with multiplicative divisor sets and few eigenvalues J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-22 J. W. Sander, T. Sander
We present a method which in principal allows to characterise all integral circulant graphs with multiplicative divisor set having a spectrum, i.e. the set of distinct eigenvalues, of any given size. We shall exemplify the method for spectra of up to four eigenvalues, also reproving some known results for three eigenvalues along the way. In particular we show that given any integral circulant graph
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The closeness eigenvalues of graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-22 Lu Zheng, Bo Zhou
For a graph G with \(u,v\in V(G)\), denote by \(d_G(u,v)\) the distance between u and v in G, which is the length of a shortest path connecting them if there is at least one path from u to v in G and is \(\infty \) otherwise. The closeness matrix of a graph G is the \(|V(G)|\times |V(G)|\) symmetric matrix \((c_G(u,v))_{u,v\in V(G}\), where \(c_G(u,v)=2^{-d_G(u,v)}\) if \(u\ne v\) and 0 otherwise.
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Combinatorial Nullstellensatz over division rings J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-23 Elad Paran
We extend Alon’s Combinatorial Nullstellensatz from polynomial rings over fields to polynomial rings over division rings and to rings of polynomial functions over centrally finite division algebras. We apply our results to extend classical theorems from additive number theory to the additive theory of division rings, where the size of algebraic sets is measured by their rank in the sense of Lam.
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Power graphs of all nilpotent groups J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-22 Sayyed Heidar Jafari, Samir Zahirović
The directed power graph \(\mathbf {{\mathcal {G}}}({\textbf{G}})\) of a group \({\textbf{G}}\) is the simple digraph with vertex set G such that \(x\rightarrow y\) if y is a power of x. The power graph \({\mathcal {G}}({\textbf{G}})\) of the group \({\textbf{G}}\) is the underlying simple graph. In this paper, we prove that Prüfer group is the only nilpotent group whose power graph does not determine
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Splitting fields of mixed Cayley graphs over abelian groups J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-21 Xueyi Huang, Lu Lu, Katja Mönius
The splitting field \(\mathbb{S}\mathbb{F}(\Gamma )\) of a mixed graph \(\Gamma \) is the smallest field extension of \(\mathbb {Q}\) which contains all eigenvalues of the Hermitian adjacency matrix of \(\Gamma \). The extension degree \([\mathbb{S}\mathbb{F}(\Gamma ):\mathbb {Q}]\) is called the algebraic degree of \(\Gamma \). In this paper, we determine the splitting fields and algebraic degrees
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Saturating systems and the rank-metric covering radius J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-22 Matteo Bonini, Martino Borello, Eimear Byrne
We introduce the concept of a rank-saturating system and outline its correspondence to a rank-metric code with a given covering radius. We consider the problem of finding the value of \(s_{q^m/q}(k,\rho )\), which is the minimum \(\mathbb {F}_q\)-dimension of a q-system in \(\mathbb {F}_{q^m}^k\) that is rank-\(\rho \)-saturating. This is equivalent to the covering problem in the rank metric. We obtain
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Plateaued functions on finite nonabelian groups J. Algebraic Comb. (IF 0.8) Pub Date : 2023-09-22 Bangteng Xu
Using the Fourier transforms at irreducible unitary representations, we introduce the plateaued functions on finite nonabelian groups, which are a generalization of plateaued functions on finite abelian groups as well as bent functions on finite (abelian or nonabelian) groups. As irreducible unitary representations of finite nonabelian groups are much more complicated than characters of finite abelian
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Derangements in wreath products of permutation groups J. Algebraic Comb. (IF 0.8) Pub Date : 2023-08-28 Vishnuram Arumugam, Heiko Dietrich, S. P. Glasby
Given a finite group G acting on a set X let \(\delta _k(G,X)\) denote the proportion of elements in G that have exactly k fixed points in X. Let \(\mathcal {S}_n\) denote the symmetric group acting on \([n]=\{1,2,\dots ,n\}\). For \(A\leqslant \mathcal {S}_m\) and \(B\leqslant \mathcal {S}_n\), the permutational wreath product \(A\wr B\) has two natural actions and we give formulas for both, \(\delta
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Regularity of powers of edge ideals of Cohen–Macaulay weighted oriented forests J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-28 Manohar Kumar, Ramakrishna Nanduri
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Subsets of virtually nilpotent groups with the SBM property J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-22 Ryan Burkhart, Isaac Goldbring
We extend Leth’s notion of subsets of the integers satisfying the standard interval measure (SIM) property to the class of virtually nilpotent groups and name the corresponding property the standard ball measure property. In order to do this, we define a natural measure on closed balls in asymptotic cones associated with such groups and show that this measure satisfies the Lebesgue density theorem
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A symmetric group action on the irreducible components of the Shi variety associated to $$W({\widetilde{A}}_n)$$ J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-15 Nathan Chapelier-Laget
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Postnikov–Stanley Linial arrangement conjecture J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-17 Shigetaro Tamura
A characteristic polynomial is an important invariant in the field of hyperplane arrangement. For the Linial arrangement of any irreducible root system, Postnikov and Stanley conjectured that all roots of the characteristic polynomial have the same real part. In relation to this conjecture, Yoshinaga obtained an explicit relationship between the characteristic quasi-polynomial and the Ehrhart quasi-polynomial
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Recovering affine linearity of functions from their restrictions to affine lines J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-14 Apoorva Khare, Akaki Tikaradze
Motivated by recent results of Tao–Ziegler [Discrete Anal. 2016] and Greenfeld–Tao (2022 preprint) on concatenating affine-linear functions along subgroups of an abelian group, we show three results on recovering affine linearity of functions \(f: V \rightarrow W\) from their restrictions to affine lines, where V, W are \({\mathbb {F}}\)-vector spaces and \(\dim V \geqslant 2\). First, if \(\dim V
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Multiple contractions of permutation arrays J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-14 Carmen Amarra, Dom Vito A. Briones, Manuel Joseph C. Loquias
Given a permutation \(\sigma \) on n symbols \(\lbrace 0, 1, \ldots , n-1 \rbrace \) and an integer \(1 \le m \le n-1\), the mth contraction of \(\sigma \) is the permutation \(\sigma ^{\textsf {CT}^m}\) on \(n-m\) symbols obtained by deleting the symbols \(n-1, n-2, \ldots , n-m\) from the cycle decomposition of \(\sigma \). The Hamming distance \(\textrm{hd}(\sigma ,\tau )\) between two permutations
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Combinatorics and preservation of conically stable polynomials J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-14 Giulia Codenotti, Stephan Gardoll, Thorsten Theobald
Given a closed, convex cone \(K\subseteq \mathbb {R}^n\), a multivariate polynomial \(f\in \mathbb {C}[\textbf{z}]\) is called K-stable if the imaginary parts of its roots are not contained in the relative interior of K. If K is the nonnegative orthant, K-stability specializes to the usual notion of stability of polynomials. We develop generalizations of preservation operations and of combinatorial
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Nonvanishing Betti numbers of edge ideals of weakly chordal graphs J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-13 José Martínez-Bernal, Oscar A. Pizá-Morales, Miguel A. Valencia-Bucio
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Integral closures of powers of sums of ideals J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-13 Arindam Banerjee, Tài Huy Hà
Let \({\mathbb {k}}\) be a field, let A and B be polynomial rings over \({\mathbb {k}}\), and let \(S= A \otimes _{\mathbb {k}}B\). Let \(I \subseteq A\) and \(J \subseteq B\) be monomial ideals. We establish a binomial expansion for rational powers of \(I+J \subseteq S\) in terms of those of I and J. Particularly, for \(u \in {\mathbb Q}_+\), we prove that $$\begin{aligned} (I+J)_u = \sum _{0 \le
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Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions J. Algebraic Comb. (IF 0.8) Pub Date : 2023-06-13 Domingos M. Cardoso, Inês Serôdio Costa, Rui Duarte