A NEW CONGRUENCE MODULO 25 FOR 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS

作者：Xia, Ernest X. W.^*

来源：Bulletin of the Australian Mathematical Society, 2015, 91(1): 41-46.

DOI：10.1017/S0004972714000768

• congruence
• 1-shell totally symmetric plane partitions
• TSPP

For any positive integer n, let f (n) denote the number of 1-shell totally symmetric plane partitions of n. Recently, Hirschhorn and Sellers ['Arithmetic properties of 1-shell totally symmetric plane partitions', Bull. Aust. Math. Soc. 89 (2014), 473-478] and Yao ['New infinite families of congruences modulo 4 and 8 for 1-shell totally symmetric plane partitions', Bull. Aust. Math. Soc. 90 (2014), 37-46] proved a number of congruences satisfied by f (n). In particular, Hirschhorn and Sellers proved that f (10n + 5) equivalent to 0 (mod 5). In this paper, we establish the generating function of f (30n + 25) and prove that f (250n + 125) equivalent to 0 (mod 25) :

• 出版日期2015-2
• 单位江苏大学