Related papers: Smith Normal Form of a Multivariate Matrix Associa…

We study macroscopic observables of large random matrices introduced by Pennington and Worah, defined by applying entry wise a non linear function on a product of matrices with independent entries. We allow the variance of the entries of…

By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated…

Given a Stirling permutation w, we introduce the mesa set of w as the natural generalization of the pinnacle set of a permutation. Our main results characterize admissible mesa sets and give closed enumerative formulas in terms of rational…

In this paper we explore determinantal representations of multiaffine polynomials and consequences for the image of various spaces of matrices under the principal minor map. We show that a real multiaffine polynomial has a definite…

A finite or infinite matrix $A$ is image partition regular provided that whenever $\mathbb N$ is finitely colored, there must be some $\vec{x}$ with entries from $\mathbb N$ such that all entries of $A\vec{x}$ are in some color class. In…

We prove a conjecture of Mills, Robbins and Rumsey [Alternating sign matrices and descending plane partitions, J. Combin. Theory Ser. A 34 (1983), 340-359] that, for any n, k, m and p, the number of nxn alternating sign matrices (ASMs) for…

We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a…

A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…

Given a suitable collection of partitions of sets, there exists a connection to easy quantum groups via intertwiner maps. A sufficient condition for this correspondence to be one-to-one are particular linear independences on the level of…

For solving the continuous Sylvester equation, a class of the multiplicative splitting iteration method is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations…

For a real affine hyperplane arrangement, we define an integer intersection matrix with a natural $q$-deformation related to the intersections of bounded chambers of the arrangement. By connecting the integer matrix to a bilinear form of…

We describe an algorithm for determining whether two convex polytopes P and Q, embedded in a lattice, are isomorphic with respect to a lattice automorphism. We extend this to a method for determining if P and Q are equivalent, i.e. whether…

We define a family of maps on lattice paths, called sweep maps, that assign levels to each step in the path and sort steps according to their level. Surprisingly, although sweep maps act by sorting, they appear to be bijective in general.…

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…

This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…

We show that all finite lattices, including non-distributive lattices, arise as stable matching lattices when all agents have path-independent choice functions. This result answers an open question of Blair~\cite{blair1988lattice}. In the…

We associate with a matrix over an arbitrary field an infinite family of matrices whose sizes vary from one to infinity; their entries are traces of powers of the original matrix. We explicitly evaluate the determinants of matrices in our…

We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…

The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type $B$ analogues are shown to have only real roots.…

Here we consider the image of the principal minor map of symmetric matrices over an arbitrary unique factorization domain $R$. By exploiting a connection with symmetric determinantal representations, we characterize the image of the…