SELF-CONJUGATE VECTOR PARTITIONS AND THE PARITY OF THE SPT-FUNCTION
SELF-CONJUGATE VECTOR PARTITIONS AND THE PARITY OF THE SPT-FUNCTION
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DOI：
10.4064/aa158-3-1
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发表时间：
2013
期刊：
影响因子：
0.7
通讯作者：
G. Andrews;F. Garvan;Jie Liang
中科院分区：
文献类型：
--
作者：
G. Andrews;F. Garvan;Jie Liang
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coecients of a certain mock theta function studied by the rst author, Dyson and Hickerson. As a result we obtain an elementary q-series proof of Ono and Folsom's results for the parity of spt(n). A number of related generating function identities are also obtained.
