Related papers: Symmetry Classes of Alternating Sign Matrices

The alternate row and column scaling algorithm applied to a positive $n\times n$ matrix $A$ converges to a doubly stochastic matrix $S(A)$, sometimes called the \emph{Sinkhorn limit} of $A$. For every positive integer $n$, a two parameter…

The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search lead to some infinite classes of disjoint weighing matrices, which in turn are shown to…

We define symmetry classes and commutation symmetries in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigate them by means of tools from the representation theory of symmetric groups S_N such as…

We consider square matrices A that commute with a fixed square matrix K, both with entries in a field F not of characteristic 2. When K^2=I, Tao and Yasuda defined A to be generalized centrosymmetric with respect to K. When K^2=-I, we…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into…

We construct six unitary trace invariants for 2 by 2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We prove two quaternionic versions of a well known…

We study square lattice space group symmetry fractionalization in a family of exactly solvable models with $\mathbb{Z}_2$ topological order in two dimensions. In particular, we have obtained a complete understanding of which distinct types…

Plane partitions in the totally symmetric self-complementary symmetry class (TSSCPP) are known to be equinumerous with n x n alternating sign matrices, but no explicit bijection is known. In this paper, we give a bijection from these plane…

It was shown recently by the authors that, for any n, there is equality between the distributions of certain triplets of statistics on nxn alternating sign matrices (ASMs) and descending plane partitions (DPPs) with each part at most n. The…

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…

The p-adic valuations of a sequence of integers T(n) counting alternating sign matrices is examined for p=2 and p=3. Symmetry properties of their graphs produce a new proof of the result that characterizes the indices for which T(n) is odd.

A sign pattern matrix is a matrix whose entries are from the set $\{+,-,0\}$. If $A$ is an $m\times n$ sign pattern matrix, the qualitative class of $A$, denoted $Q(A)$, is the set of all real $m\times n$ matrices $B=[b_{i,j}]$ with…

A synaptic algebra is a common generalization of several ordered algebraic structures based on algebras of self-adjoint operators, including the self-adjoint part of an AW*-algebra. In this paper we prove that a synaptic algebra A has the…

A graph is said to be symmetric if its automorphism group is transitive on its arcs. Guo et al. (Electronic J. Combin. 18, \#P233, 2011) and Pan et al. (Electronic J. Combin. 20, \#P36, 2013) determined all pentavalent symmetric graphs of…

The sign patterns of inverse doubly-nonnegative matrices are examined. A necessary and sufficient condition is developed for a sign matrix to correspond to an inverse doubly-nonnegative matrix. In addition, for a doubly-nonnegative matrix…

We study distinct $(0,1)$ matrices $A$ and $B$, called \textit{Gram mates}, such that $AA^T=BB^T$ and $A^TA=B^TB$. We characterize Gram mates where one can be obtained from the other by changing signs of some positive singular values. We…

This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…

Families of alternating knots (links) and tangles are studied using as building block the conway defined as the twisting of two strands. The regular representation of knots assumes the projection has the minimal number of overpassings, and…

We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…