NDLI: Properties of the nonsymmetric Robinson–Schensted

Content Provider	Springer Nature Link
Author	Haglund, James Mason, Sarah Remmel, Jeffrey
Copyright Year	2012
Abstract	We introduce a generalization of the Robinson–Schensted–Knuth insertion algorithm for semi-standard augmented fillings whose basement is an arbitrary permutation σ∈S $_{ n }$. If σ is the identity, then our insertion algorithm reduces to the insertion algorithm introduced by the second author (Sémin. Lothar. Comb. 57:B57e, 2006) for semi-standard augmented fillings and if σ is the reverse of the identity, then our insertion algorithm reduces to the original Robinson–Schensted–Knuth row insertion algorithm. We use our generalized insertion algorithm to obtain new decompositions of the Schur functions into nonsymmetric elements called generalized Demazure atoms (which become Demazure atoms when σ is the identity). Other applications include Pieri rules for multiplying a generalized Demazure atom by a complete homogeneous symmetric function or an elementary symmetric function, a generalization of Knuth’s correspondence between matrices of non-negative integers and pairs of tableaux, and a version of evacuation for composition tableaux whose basement is an arbitrary permutation σ.
Starting Page	285
Ending Page	327
Page Count	43
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	38
Issue Number	2
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2012-10-20
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Symmetric functions Permutations Nonsymmetric Macdonald polynomials Demazure atoms Permuted basement fillings Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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