Related papers: Asymptotic enumeration of symmetric integer matric…
We analyse the asymptotic symmetries of Maxwell theory at spatial infinity through the Hamiltonian formalism. Precise, consistent boundary conditions are explicitly given and shown to be invariant under asymptotic angle-dependent…
Symmetric edge polytopes, also called adjacency polytopes, are lattice polytopes determined by simple undirected graphs. We introduce the integer array \(\mathrm{maxf}(n,m)\) giving the maximum number of facets of a symmetric edge polytope…
This paper investigates the number of monic integer polynomials of degree $n$ whose roots are all real and positive. We establish an asymptotic formula for the case of fixed trace by estimating the number of integer sequences satisfying…
We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of…
In this note, we show that the norm of an $n\times n$ random jointly exchangeable matrix with zero diagonal can be estimated in terms of the norm of its $n/2\times n/2$ submatrix located in the top right corner. As a consequence, we prove a…
We present a new probabilistic proof of Otter's asymptotic formula for the number of unlabelled trees with a given number of vertices. We additionally prove a new approximation result, showing that the total variation distance between…
Recently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior of several algebraic and homological invariants along such…
We show, using a hybrid analysis/linear algebra argument, that the diagonal vector of an infinite symmetric matrix over ${\mathbb Z}_2$ is contained in the range of the matrix. We apply this result to an extension, to the countable infinite…
Does a given system of linear equations with nonnegative constraints have an integer solution? This is a fundamental question in many areas. In statistics this problem arises in data security problems for contingency table data and also is…
Given a finite group $G$, the invariably generating graph of $G$ is defined as the undirected graph in which the vertices are the nontrivial conjugacy classes of $G$, and two classes are adjacent if and only if they invariably generate $G$.…
We introduce matrix algebra of subsets in metric spaces and we apply it to improve results of Yamauchi and Davila regarding Asymptotic Property C. Here is a representative result: Suppose $X$ is an $\infty$-pseudo-metric space and $n\ge 0$…
Cyclic monotone independence is an algebraic notion of noncommutative independence, introduced in the study of multi-matrix random matrix models with small rank. Its algebraic form turns out to be surprisingly close to monotone…
We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently…
We show that the infinite symmetric product of a connected graded-commutative algebra over the rationals is naturally isomorphic to the free graded-commutative algebra on the positive degree subspace of the original algebra. In particular,…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
Let $M=(m_{ij})$ be a symmetric matrix of order $n$ whose elements lie in an arbitrary field $\mathbb{F}$, and let $G$ be the graph with vertex set $\{1,\ldots,n\}$ such that distinct vertices $i$ and $j$ are adjacent if and only if $m_{ij}…
We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with source term containing two distinct eigenvalues. These conditions are shown to be equivalent to the existence of a…
Motivated by the necessities of the invariant theory of binary forms J. J. Sylvester constructed in 1878 for each graph with possible multiple edges but without loops its symmetrized graph monomial which is a polynomial in the vertex labels…
We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at least one other graph with the same Smith normal form…
Many aspects of the asymptotics of Plancherel distributed partitions have been studied in the past fifty years, in particular the limit shape, the distribution of the longest rows, connections with random matrix theory and characters of the…