Cylindric Schur functions
Combinatorics
2023-11-14 v1 Representation Theory
Abstract
We generalize several classical results about Schur functions to the family of cylindric Schur functions. First, we give a combinatorial proof of a Murnaghan--Nakayama formula for expanding cylindric Schur functions in the power-sum basis. We also explore some cases where this formula is cancellation-free. The second result is polynomiality of Kostka coefficients associated with stretched row-flagged skew Schur functions. This implies polynomiality of stretched cylindric Kostka coefficients. This generalizes a result by E. Rassart from 2004. Finally, we also show the saturation property for the row-flagged skew Kostka coefficients which also implies the saturation property for cylindric Schur functions.
Cite
@article{arxiv.2311.07382,
title = {Cylindric Schur functions},
author = {Per Alexandersson and Ezgi Kantarci Oğuz},
journal= {arXiv preprint arXiv:2311.07382},
year = {2023}
}
Comments
30 pages, comments welcome!