Complete flagged homogeneous polynomials
Combinatorics
2023-05-08 v1
Abstract
We introduce a new basis for the polynomial ring which lifts the complete homogeneous symmetric polynomials while retaining representation theoretic significance. Using a specialized RSK algorithm we give an explicit nonnegative expansion into key polynomials and, generalizing the special rim hook tabloids of E\u{g}ecio\u{g}lu and Remmel, give an explicit signed expansion for key polynomials into this new basis.
Cite
@article{arxiv.2305.03241,
title = {Complete flagged homogeneous polynomials},
author = {Henry Ehrhard},
journal= {arXiv preprint arXiv:2305.03241},
year = {2023}
}