The shifted plactic monoid
Combinatorics
2009-01-21 v2
Abstract
We introduce a shifted analog of the plactic monoid of Lascoux and Sch\"utzenberger, the \emph{shifted plactic monoid}. It can be defined in two different ways: via the \emph{shifted Knuth relations}, or using Haiman's mixed insertion. Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion of a Schur -function; a shifted counterpart of the Lascoux-Sch\"utzenberger theory of noncommutative Schur functions in plactic variables; a characterization of shifted tableau words; and more.
Cite
@article{arxiv.0811.2057,
title = {The shifted plactic monoid},
author = {Luis Serrano},
journal= {arXiv preprint arXiv:0811.2057},
year = {2009}
}
Comments
32 pages, youngtab.sty required