相关论文: Harmonic functions on multiplicative graphs and in…

In this paper, we study discrete harmonic functions on infinite penny graphs. For an infinite penny graph with bounded facial degree, we prove that the volume doubling property and the Poincar\'e inequality hold, which yields the Harnack…

We study the symmetric function and polynomial combinatorial invariants of Hopf algebras of permutations, posets and graphs. We investigate their properties and the relations among them. In particular, we show that the chromatic symmetric…

We review and present new studies on the relation between the partition functions of integrable lattice models and symmetric polynomials, and its combinatorial representation theory based on the correspondence, including our work. In…

This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…

In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from $C^{\infty}$…

We compute an explicit $e$-positive formula for the chromatic symmetric function of a lollipop graph, $L_{m,n}$. From here we deduce that there exist countably infinite distinct $e$-positive, and hence Schur-positive, bases of the algebra…

Given a holomorphic iterated function scheme with a finite symmetry group $G$, we show that the associated dynamical zeta function factorizes into symmetry-reduced analytic zeta functions that are parametrized by the unitary irreducible…

This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young…

We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation…

Using the combinatorics of $\alpha$-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that…

For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…

In this paper we study spectral zeta functions associated to finite and infinite graphs. First we establish a meromorphic continuation of these functions under some general conditions. Then we study special values in the case of standard…

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in…

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…

Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal harmonics. Motivated by the Stanley--Stembridge…

We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical ``square'' of…

In this paper, we propose an algebraic approach to determine whether two non-isomorphic caterpillar trees can have the same symmetric function generalization of the chromatic polynomial. On the set of all composition on integers, we…

It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…

Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by…