Jack symmetric functions and some combinatorial properties of young symmetrizers

Some Results about the Contractions and the Pendant Pairs of a Submodular System

Submodularity is an important  property of set functions with deep theoretical results  and various  applications. Submodular systems appear in many applicable area, for example machine learning, economics, computer vision, social science, game theory and combinatorial optimization.  Nowadays submodular functions optimization has been attracted by many researchers.  Pendant pairs of a symmetric...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

A Recursion and a Combinatorial Formula for Jack Polynomials

The Jack polynomials Jλ(x; α) form a remarkable class of symmetric polynomials. They are indexed by a partition λ and depend on a parameter α. One of their properties is that several classical families of symmetric functions can be obtained by specializing α, e.g., the monomial symmetric functions mλ (α = ∞), the elementary functions eλ′ (α = 0), the Schur functions sλ (α = 1) and finally the t...

On the Matchings-Jack Conjecture for Jack Connection Coefficients Indexed by Two Single Part Partitions

This article is devoted to the study of Jack connection coefficients, a generalization of the connection coefficients of the classical commutative subalgebras of the group algebra of the symmetric group closely related to the theory of Jack symmetric functions. First introduced by Goulden and Jackson (1996) these numbers indexed by three partitions of a given integer n and the Jack parameter α ...

Anisotropic Young Diagrams and Jack Symmetric Functions

Λ:λրΛ(cα(b) + u)(cα(b) + v)κα(λ,Λ)φ(Λ) = (nα + uv) φ(λ), where cα(b) is the α-content of a new box b = Λ \ λ. If α = 1, this identity implies the existence of an interesting family of positive definite central functions on the infinite symmetric group. The approach is based on the interpretation of a Young diagram as a pair of interlacing sequences, so that analytic techniques may be used to so...