1997/12/01 by David M. Bressoud, Bressoud, David M.
Mathematics · #05A17 #05E10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A17 #msc:05E10
paper · pdf · doi:10.48550/arxiv.math/9712208
arxiv created 1997/12/01 · openalex publication_date 1997/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Major Percy A. MacMahon's first paper on plane partitions 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 and Macdonald employing his knowledge of symmetric functions. 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.