Transformations of Border Strips and Schur Function Determinants 
 
Authors:  Email author<" target="_blank">William Y C ChenEmail author< GuoGuang Yan Arthur L B Yang 
 
Institution:  (1) Center for Combinatorics, LPMC, Nankai University, Tianjin, 300071, P. R. China 
 
Abstract:  We introduce the notion of the cutting strip of an outside decomposition of a skew shape, and show that cutting strips are in onetoone 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 JacobiTrudi 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. 
 
Keywords:  Young diagram border strip outside decomposition Schur function determinants JacobiTrudi identity Giambelli identity LascouxPragacz identity 
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