Genomic Tableaux
Combinatorics
2017-07-11 v1 Algebraic Geometry
Abstract
We explain how genomic tableaux [Pechenik-Yong '15] are a semistandard complement to increasing tableaux [Thomas-Yong '09]. From this perspective, one inherits genomic versions of jeu de taquin, Knuth equivalence, infusion and Bender-Knuth involutions, as well as Schur functions from (shifted) semistandard Young tableaux theory. These are applied to obtain new Littlewood-Richardson rules for K-theory Schubert calculus of Grassmannians (after [Buch '02]) and maximal orthogonal Grassmannians (after [Clifford-Thomas-Yong '14], [Buch-Ravikumar '12]). For the unsolved case of Lagrangian Grassmannians, sharp upper and lower bounds using genomic tableaux are conjectured.
Cite
@article{arxiv.1603.08490,
title = {Genomic Tableaux},
author = {Oliver Pechenik and Alexander Yong},
journal= {arXiv preprint arXiv:1603.08490},
year = {2017}
}
Comments
30 pages, color figures