Related papers: Stanley symmetric functions and Peterson algebras

We study flat deformations of quotients of a polynomial algebra in a class of graded commutative associative algebras. Functional equations and their solutions in terms of theta functions play important role in these studies. An analog of…

We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…

Abstract characterizations of Menger algebras of partial $n$-place functions defined on a set $A$ and closed under the set-theoretic difference functions treatment as subsets of the Cartesian product $A^{n+1}$ are given.

In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which…

We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of…

In the article random functions in modules over the octonion algebra and Cayley-Dickson algebras are investigated. For their study transition measures with values in the octonion algebra and Cayley-Dickson algebras are used. Stochastic…

The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two…

The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the…

These are (not updated) notes from the lectures I gave at the NATO ASI ``Symmetric Functions 2001'' at the Isaac Newton Institute in Cambridge (June 25 -- July 6, 2001). Their goal is an informal introduction to asymptotic combinatorics…

Let $I$ be a monomial almost complete intersection ideal of a polynomial algebra $S$ over a field. Then Stanley's Conjecture holds for $S/I$ and $I$.

We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.

Stanley associated with a graph G a symmetric function X_G which reduces to G's chromatic polynomial under a certain specialization of variables. He then proved various theorems generalizing results about the chromatic polynomial, as well…

This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description…

We give a new formula for the irreducible spin characters of the symmetric groups. This formula is analogous to Stanley's character formula for the usual (linear) characters of the symmetric groups.

This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…

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.

This paper is about a family of symmetric rational functions that form a one-parameter generalization of the classical Hall-Littlewood polynomials. We introduce two sets of (skew and non-skew) functions that are akin to P and Q…

Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main…

Let $I\supsetneq J$ be two monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . We study when the Stanley Conjecture holds for $I/J$ using the recent result of \cite{IKM} concerning the…

Stanley and Grinberg introduced the symmetric function associated to digraphs, called the Redei-Berge symmetric function. In [8] is shown that this symmetric function arises from a suitable structure of combinatorial Hopf algebra on…