Multiline queues with spectral parameters
Combinatorics
2023-05-09 v2
Abstract
Using the description of multiline queues as functions on words, we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues. We show that the spectral weight of a word is invariant under a natural action of the symmetric group, giving a proof of the commutativity conjecture of Arita, Ayyer, Mallick, and Prolhac. We give a determinant formula for the spectral weight of a word, which gives a proof of a conjecture of the first author and Linusson.
Cite
@article{arxiv.1810.08157,
title = {Multiline queues with spectral parameters},
author = {Erik Aas and Darij Grinberg and Travis Scrimshaw},
journal= {arXiv preprint arXiv:1810.08157},
year = {2023}
}
Comments
44 pages, 6 figures; see the ancillary file for a long version