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- Title
PARITY RESULTS FOR PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER OF TIMES.
- Authors
HIRSCHHORN, MICHAEL D.; SELLERS, JAMES A.
- Abstract
We consider the function $f(n)$ that enumerates partitions of weight $n$ wherein each part appears an odd number of times. Chern ['Unlimited parity alternating partitions', Quaest. Math. (to appear)] noted that such partitions can be placed in one-to-one correspondence with the partitions of $n$ which he calls unlimited parity alternating partitions with smallest part odd. Our goal is to study the parity of $f(n)$ in detail. In particular, we prove a characterisation of $f(2n)$ modulo 2 which implies that there are infinitely many Ramanujan-like congruences modulo 2 satisfied by the function $f.$ The proof techniques are elementary and involve classical generating function dissection tools.
- Subjects
PARTITIONS (Mathematics); ODD numbers; PARITY-check matrix; GENERATING functions; MATHEMATICS theorems
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p51
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718001041