TY - JOUR
T1 - Genomic tableaux
AU - Pechenik, Oliver
AU - Yong, Alexander
N1 - We thank Hugh Thomas for many conversations which helped to make this project possible. We thank the referees for helpful comments that improved the exposition of this paper. OP was supported by an NSF Graduate Research Fellowship, and Illinois Distinguished Fellowship from the University of Illinois, and NSF MCTP grant DMS 0838434. AY was supported by NSF grants and a Helen Corley Petit fellowship at UIUC.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84992176831
UR - https://www.scopus.com/pages/publications/84992176831#tab=citedBy
U2 - 10.1007/s10801-016-0720-8
DO - 10.1007/s10801-016-0720-8
M3 - Article
AN - SCOPUS:84992176831
SN - 0925-9899
VL - 45
SP - 649
EP - 685
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 3
ER -