منابع مشابه
Schur-Positivity in a Square
Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem. In this paper we study the Schur-positivity of a family of symmetric functions. Given a partition ν, we denote by νc its complement in a square partition (mm). We conjecture a Schur-positivity criterion for symmetric functions of the form sμ′sμc − sν′sνc , where ν is a partitio...
متن کاملNecessary Conditions for Schur-positivity
In recent years, there has been considerable interest in showing that certain conditions on skew shapes A and B are sufficient for the difference sA − sB of their skew Schur functions to be Schur-positive. We determine necessary conditions for the difference to be Schur-positive. Our conditions are motivated by those of Reiner, Shaw and van Willigenburg that are necessary for sA = sB , and we d...
متن کامل2 00 5 Schur Positivity and Schur Log - Concavity
We prove Okounkov’s conjecture, a conjecture of Fomin-FultonLi-Poon, and a special case of Lascoux-Leclerc-Thibon’s conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. An alternative proof of this result is provided. We also give an intriguing log-concavity property of Schur functions. 1. Schur positivity conjectures The ring of...
متن کاملSchur Positivity and Kirillov–Reshetikhin Modules
In this note, inspired by the proof of the Kirillov–Reshetikhin conjecture, we consider tensor products of Kirillov–Reshetikhin modules of a fixed node and various level. We fix a positive integer and attach to each of its partitions such a tensor product. We show that there exists an embedding of the tensor products, with respect to the classical structure, along with the reverse dominance rel...
متن کاملPositivity results on ribbon Schur function differences
There is considerable current interest in determining when the difference of two skew Schur functions is Schur positive. While the general solution for ribbon Schur functions seems out of reach at present, we determine necessary and sufficient conditions for multiplicity-free ribbons, i.e. those whose expansion as a linear combination of Schur functions has all coefficients either zero or one. ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/3796