Identifying Young diagrams among residue multisets
Representation Theory
2024-04-23 v3 Combinatorics
Abstract
To any Young diagram we can associate the multiset of residues of all its nodes. This paper is concerned with the inverse problem: given a multiset of elements of Z/eZ, does it comes from a Young diagram? We give a full solution in level one and a partial answer in higher levels for Young multidiagrams, using Fayers's notions of core block and weight of a multipartition. We apply the result in level one to study a shift operation on partitions.
Cite
@article{arxiv.2011.13872,
title = {Identifying Young diagrams among residue multisets},
author = {Salim Rostam},
journal= {arXiv preprint arXiv:2011.13872},
year = {2024}
}
Comments
42 pages. v3: minor changes, final version, to appear in Annals of Combinatorics