NDLI: Transformations of Border Strips and Schur Function Determinants

Content Provider	Springer Nature Link
Author	Chen, William Y. C. Yan, Guo Guang Yang, Arthur L. B.
Copyright Year	2005
Abstract	We introduce the notion of the cutting strip of an outside decomposition of a skew shape, and show that cutting strips are in one-to-one correspondence with outside decompositions for a given skew shape. Outside decompositions are introduced by Hamel and Goulden and are used to give an identity for the skew Schur function that unifies the determinantal expressions for the skew Schur functions including the Jacobi-Trudi determinant, its dual, the Giambelli determinant and the rim ribbon determinant due to Lascoux and Pragacz. Using cutting strips, one obtains a formula for the number of outside decompositions of a given skew shape. Moreover, one can define the basic transformations which we call the twist transformation among cutting strips, and derive a transformation theorem for the determinantal formula of Hamel and Goulden. The special case of the transformation theorem for the Giambelli identity and the rim ribbon identity was obtained by Lascoux and Pragacz. Our transformation theorem also applies to the supersymmetric skew Schur function.
Starting Page	379
Ending Page	394
Page Count	16
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	21
Issue Number	4
e-ISSN	15729192
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Young diagram border strip outside decomposition Schur function determinants Jacobi-Trudi identity Giambelli identity Lascoux-Pragacz identity Computer Science Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Combinatorics Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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