Higher order SPT functions for overpartitions, overpartitions with smallest part even, and partitions with smallest part even and without repeated odd parts
نویسندگان
چکیده
منابع مشابه
Partitions and Overpartitions with Attached Parts
We show how to interpret a certain q-series as a generating function for overpartitions with attached parts. A number of families of partition theorems follow as corollaries.
متن کاملOverpartitions with Restricted Odd Differences
We use q-difference equations to compute a two-variable q-hypergeometric generating function for overpartitions where the difference between two successive parts may be odd only if the larger part is overlined. This generating function specializes in one case to a modular form, and in another to a mixed mock modular form. We also establish a two-variable generating function for the same overpar...
متن کاملArithmetic Properties of Overpartitions into Odd Parts
In this article, we consider various arithmetic properties of the function po(n) which denotes the number of overpartitions of n using only odd parts. This function has arisen in a number of recent papers, but in contexts which are very different from overpartitions. We prove a number of arithmetic results including several Ramanujan-like congruences satisfied by po(n) and some easily-stated ch...
متن کاملCounting Even and Odd Partitions
1. Introduction. It is a lovely fact that n] = f1; 2; : : : ; ng, n 1, has as many subsets X with an even cardinality jXj as those with an odd cardinality, namely 2 n?1 of both. To prove it, pair every subset X with X 1 where X 1 is Xnf1g if 1 2 X and X f1g if 1 6 2 X. Then X 7 ! X 1 is an involution that changes the parity of jXj and the result follows. More generally, in enumerative combinato...
متن کاملON THE NUMBER OF EVEN AND ODD STRINGS ALONG THE OVERPARTITIONS OF n
A partition of a non-negative integer n is a non-increasing sequence of positive integers whose sum is n. For example, The 5 partitions of 4 are 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. To explain Ramanujan’s famous three partition congruences, the partition statistics, the rank (resp. the crank) were introduced by Dyson [8] (resp. Andrews and Garvan [3]). Atkin and Garvan [5] initiated t...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.10.011