Geodesic
A generalization of the Littlewood-Richardson rule
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 4, pp. 379-394.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: keywords Young diagram, border strip, outside decomposition, Schur function determinants, Jacobi-trudi identity, giambelli identity, lascoux-pragacz identity 
@article{JAC_2005__21_4_a3,
     author = {Chen, William Y.C. and Yan, Guo-Guang and Yang, Arthur L.B.},
     title = {A generalization of the {Littlewood-Richardson} rule},
     journal = {Journal of Algebraic Combinatorics},
     pages = {379--394},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2005__21_4_a3/}
}
TY  - JOUR
AU  - Chen, William Y.C.
AU  - Yan, Guo-Guang
AU  - Yang, Arthur L.B.
TI  - A generalization of the Littlewood-Richardson rule
JO  - Journal of Algebraic Combinatorics
PY  - 2005
SP  - 379
EP  - 394
VL  - 21
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2005__21_4_a3/
LA  - en
ID  - JAC_2005__21_4_a3
ER  - 
%0 Journal Article
%A Chen, William Y.C.
%A Yan, Guo-Guang
%A Yang, Arthur L.B.
%T A generalization of the Littlewood-Richardson rule
%J Journal of Algebraic Combinatorics
%D 2005
%P 379-394
%V 21
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2005__21_4_a3/
%G en
%F JAC_2005__21_4_a3
Chen, William Y.C.; Yan, Guo-Guang; Yang, Arthur L.B. A generalization of the Littlewood-Richardson rule. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 4, pp. 379-394. http://geodesic.mathdoc.fr/item/JAC_2005__21_4_a3/