논문KCI 등재
Generalization of the sign reversing involution on the special rim hook tableaux
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Egecioglu and Remmel [1] gave a combinatorial interpretation for the entries of the inverse Kostka matrix K-1. Using this interpretation Sagan and Lee [8] constructed a sign reversing involution on special rim hook tableaux. In this paper we generalize Sagan and Lee's algorithm on special rim hook tableaux to give a combinatorial partial proof of K-1 K=I.
Abstract
Egecioglu and Remmel [1] gave a combinatorial interpretation for the entries of the inverse Kostka matrix K-1. Using this interpretation Sagan and Lee [8] constructed a sign reversing involution on special rim hook tableaux. In this paper we generalize Sagan and Lee's algorithm on special rim hook tableaux to give a combinatorial partial proof of K-1 K=I.
참고문헌 (11)
- O. Egecioglu, "A combinatorial interpretation of the inverse Kostka matrix", Linear Multilinear Algebra, 26, pp.59~84 (1990)
- W. Fulton, "Young Tableaux" (1999), Cambridge University Press
- I. Gessel, "Binomial determinants, paths, and hook length for-mulae", Adv. Math., 58, pp.300~321 (1985)
- I. Gessel, "Determinants, paths, and plane partitions, in prepa-ration", ~
- B. Lindstrom, "On the vector representation of induced matroids", Bull. Lond. Math. Soc., 5, pp.85~90 (1973)
- I. G. Macdonald, "Symmetric functions and Hall polynomials, 2nd edition" (1995), Oxford University Press
- B. Sagan, "The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edition" (2001), Springer-Verlag
- B. Sagan, "An algorithmic sign-reversing involution for special rim-hook tableaux", J. Algorithms, 59, pp.149~161 (2006)
- R. P. Stanley, "Enumerative Combinatorics, Volume 2" (1999), Cambridge University Press
- D. Stanton, "A Schensted correspondence for rim hook tableaux", J. Combin. Theory Ser., A40, pp.211~247 (1985)
- D. White, "A bijection proving orthogonality of the characters of Sn", Adv. Math., 50, pp.160~186 (1983)
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