Related papers: $P$-partitions with flags and back stable quasisym…

A sequence of representations \(V_n\) of the symmetric group \(S_n\) is called representation (multiplicity) stable if, after some \(n\), the irreducible decomposition of \(V_n\) stabilizes. In particular, Church, Ellenburg and Farb (2015)…

Physical and mathematical applications of fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we…

Smith normal form evaluations found by Bessenrodt and Stanley for some Hankel matrices of q-Catalan numbers are proven in two ways. One argument generalizes the Bessenrodt-Stanley results for the Smith normal form of a certain multivariate…

Given a $\mathfrak{g}$-action on a Poisson manifold $(M, \pi)$ and an equivariant map $J: M \rightarrow \mathfrak{h}^*,$ for $\mathfrak{h}$ a $\mathfrak{g}$-module, we obtain, under natural compatibility and regularity conditions previously…

This article is an extensive study of partitions with fixed number of odd and even-indexed odd parts. We use these partitions to generalize recent results of C. Savage and A. Sills. Moreover, we derive explicit formulas for generating…

Hazewinkel proved the Ditters conjecture that the algebra of quasisymmetric functions over the integers is free commutative by constructing a nice polynomial basis. In this paper we prove a structure theorem for the algebra of peak…

This paper develops the theory of enriched toric $[\vec{D}]$-partitions. Whereas Stembridge's enriched $P$-partitions give rises to the peak algebra which is a subring of the ring of quasi-symmetric functions $\text{QSym}$, our enriched…

The partition function of composite bosons ("cobosons" for short) is calculated in the canonical ensemble, with the Pauli exclusion principle between their fermionic components included in an exact way through the finite temperature…

An extension of the method and results of A. Schwarz for evaluating the partition function of a quadratic functional is presented. This enables the partition functions to be evaluated for a wide class of quadratic functionals of interest in…

We introduce Lipschitz functions on a finite partially ordered set $P$ and study the associated Lipschitz polytope $L(P)$. The geometry of $L(P)$ can be described in terms of descent-compatible permutations and permutation statistics that…

This work deals with a new generalization of $r$-Stirling numbers using $l$-tuple of permutations and partitions called $(l,r)$-Stirling numbers of both kinds. We study various properties of these numbers using combinatorial interpretations…

The $n^{th}$ partial flag incidence algebra of a poset $P$ is the set of functions from $P^n$ to some ring which are zero on non-partial flag vectors. These partial flag incidence algebras for $n>2$ are not commutative, not unitary, and not…

Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…

The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.

We give a probabilistic interpretation of the coefficients of the elementary symmetric function expansion of the chromatic quasisymmetric function for any unit interval graph. As a corollary, we prove the Stanley--Stembridge conjecture.

P\'olya's enumeration theorem is concerned with counting labeled sets up to symmetry. Given a finite group acting on a finite set of labeled elements it states that the number of labeled sets up to symmetry is given by a polynomial in the…

In this note, we provide a simple derivation of expressions for the restricted partition function and its polynomial part. Our proof relies on elementary algebra on rational functions and a lemma that expresses the polynomial part as an…

In his work on P-partitions, Stembridge defined the algebra of peak functions Pi, which is both a subalgebra and a retraction of the algebra of quasi-symmetric functions. We show that Pi is closed under coproduct, and therefore a Hopf…

We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…

We begin with the observation that the signed generalized Stirling polynomials $P_k(m,x)$, which occur in a generalization of Malmsten's integral, reduce to the falling factorials when $k=m$. The structure of these generalized Stirling…