Some results on bipartitions with 3-core
Some results on bipartitions with 3-core
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DOI：
10.1016/j.jnt.2013.12.007
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发表时间：
2014-06
影响因子：
0.7
通讯作者：
Bernard L. S. Lin
中科院分区：
文献类型：
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作者：
Bernard L. S. Lin
本文研究了3-核双划分的算术性质。设A3（n）表示n的3-核的二划分数.我们将证明A3（n）的模5同余的一个无限族.我们还对A3（8 n+ 6）建立了一个令人惊讶的模14同余.最后证明了：如果u（n）表示非负整数n的x2 + y2 + 3 z2 + 3 t2形式的表示数，其中x，y，z，t∈ Z，则u（6 n+ 5）= 12 A3（2n + 1）.
In this paper, we investigate the arithmetic properties of bipartitions with 3-core. Let A 3 (n) denote the number of bipartitions with 3-core of n. We will prove one infinite family of congruences modulo 5 for A 3 (n). We also establish one surprising congruence modulo 14 for A 3 (8 n+ 6). Finally, we prove that, if u (n) denotes the number of representations of a nonnegative integer n in the form x 2+ y 2+ 3 z 2+ 3 t 2 with x, y, z, t∈ Z, then u (6 n+ 5)= 12 A 3 (2 n+ 1).