Annals of Combinatorics 10 (2006)On a Formula for the Kostka Numbers Mathias Lederer Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany Received January 7, 2005 AMS Subject Classification: 05E05, 05E10 Abstract. From Kostant's multiplicity formula for general linear groups, one can derive a formula for the Kostka numbers. In this note we give a combinatorial proof of this formula. Keywords: Young tableaux, Kostka numbers, partitions of integers References 1. W. Fulton, Young Tableaux, In: London Mathematical Society Student Texts, Vol. 35, Cambridge University Press, Cambridge, 1997. 2. W. Fulton and J. Harris, Representation Theory, In: Graduate Texts in Mathematics, Vol. 129, Springer-Verlag, New York, 1991. 3. B. Gordon, A proof of the Bender-Knuth conjecture, Pacific J. Math. 108 (1) (1983) 99–113. 4. D.E. Knuth, Permutations, matrices, and generalized Young tableaux, Pacific J. Math. 34 (1970) 709–727. 5. B. Kostant, A formula for the multiplicity of a weight, Trans. Amer. Math. Soc. 93 (1959) 53–73. 6. C. Krattenthaler, The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux, Mem. Amer. Math. Soc. 115 (552) (1995). 7. C. Krattenthaler, Identities for classical group characters of nearly rectangular shape, J. Algebra 209 (1) (1998) 1–64. 8. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd Edition, Oxford University Press, Oxford, 1995. 9. P.A. MacMahon, Combinatory Analysis, 2 Vols., Cambridge University Press, Cambridge, 1915–1916. 10. B.E. Sagan, The ubiquitous Young tableau, In: Invariant Theory and Tableaux, D. Stanton Ed., Springer-Verlag, New York, (1990) pp. 262–298. 11. R.P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, 1999. |