Some conjectures on the Schur expansion of Jack polynomials

نویسندگان

چکیده

We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found these bases, including Eulerian numbers, Stirling quasi-Yamanouchi tableaux, and rook boards. These also lead further about fundamental quasisymmetric expansions which we prove special cases.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Some new families of definite polynomials and the composition conjectures

The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...

متن کامل

The Schur Expansion of Macdonald Polynomials

Building on Haglund’s combinatorial formula for the transformed Macdonald polynomials, we provide a purely combinatorial proof of Macdonald positivity using dual equivalence graphs and give a combinatorial formula for the coefficients in the Schur expansion.

متن کامل

On Some Orthogonal Functions Generalizing Jack Polynomials

The rational Cherednik algebra H is a certain algebra of differential-reflection operators attached to a complex reflection group W . Each irreducible representation S of W corresponds to a standard module M(λ) for H. This paper deals with the infinite family G(r, p, n) of complex reflection groups; our goal is to study the standard modules using a commutative subalgebra t of H discovered by Du...

متن کامل

An Identity of Jack Polynomials

In this work we give an alterative proof of one of basic properties of zonal polynomials and generalised it for Jack polynomials

متن کامل

Some conjectures for Macdonald polynomials of type

We present conjectures giving formulas for the Macdonald polynomials of type B, C, D which are indexed by a multiple of the first fundamental weight. The transition matrices between two different types are explicitly given. Introduction Among symmetric functions, the special importance of Schur functions comes from their intimate connection with representation theory. Actually the irreducible p...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: The Journal of Combinatorics

سال: 2021

ISSN: ['2150-959X', '2156-3527']

DOI: https://doi.org/10.4310/joc.2021.v12.n2.a2