Abstract
Based on the combinatorial proof of Schur's partition theorem given by Bressoud, and the combinatorial proof of Alladi's partition theorem given by Padmavathamma, Raghavendra and Chandrashekara, we obtain a bijective proof of a partition theorem of Alladi, Andrews and Gordon.
Highlights
In 1926, Schur [15] proved one of the most profound results in the theory of partitions, which can be stated as follows.Theorem 1.1 (Schur)
Based on the combinatorial proof of Schur’s partition theorem given by Bressoud, and the combinatorial proof of Alladi’s partition theorem given by Padmavathamma, Raghavendra and Chandrashekara, we obtain a bijective proof of a partition theorem of Alladi, Andrews and Gordon
The objective of this paper is to provide a bijective proof of Theorem 1.3
Summary
In 1926, Schur [15] proved one of the most profound results in the theory of partitions, which can be stated as follows.Theorem 1.1 (Schur). Let B(n) be the number of partitions of n into distinct parts ≡ 2, 4, 5 (mod 6). Let C(n) be the number of partitions of n into distinct parts λ1 > λ2 > λ3 > · · · where no part equals 1 or 3, and λi − λi+1 6 with strict inequality if λi ≡ 6, 7 or 9 ( mod 6).
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