Geodesic
Elementary proof of MacMahon's conjecture
Journal of Algebraic Combinatorics, Tome 7 (1998) no. 3, pp. 253-257.

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

Summary: Major Percy A. MacMahon"s first paper on plane partitions [4] included a conjectured generating function for symmetric plane partitions. This conjecture was proven almost simultaneously by George Andrews and Ian Macdonald, Andrews using the machinery of basic hypergeometric series [1] and Macdonald employing his knowledge of symmetric functions [3]. The purpose of this paper is to simplify Macdonald"s proof by providing a direct, inductive proof of his formula which expresses the sum of Schur functions whose partitions fit inside a rectangular box as a ratio of determinants.
Keywords: plane partition, symmetric plane partition, Schur function 
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     title = {Elementary proof of {MacMahon's} conjecture},
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Bressoud, David M. Elementary proof of MacMahon's conjecture. Journal of Algebraic Combinatorics, Tome 7 (1998) no. 3, pp. 253-257. http://geodesic.mathdoc.fr/item/JAC_1998__7_3_a4/