WebAug 1, 2024 · In a previous paper, we studied an overpartition analogue of Gaussian polynomials as the generating function for overpartitions fitting inside an mn rectangle. ... Int. J. Number Theory, 6 (2010) 785-798. Google Scholar Cross Ref; br0170 B. Sagan, Unimodality and the reflection principle, Ars Combin., 48 (1998) 65-72. WebAn overpartition of n is a non-increasing sequence of positive integers whose sum is n in which the first occurrence of a number may be overlined. In this article, we investigate the arithmetic behavior of b"k(n) modulo powers of 2, where b"k(n) is the ...

On the number of l -regular overpartitions - World Scientific

WebJul 9, 2024 · An overpartition of a non-negative integer n is a partition of n in which the first occurrence of a number may be over lined. ... Journal of Number Theory 148: 62–72. … WebAn l -regular overpartition of n is an overpartition of n into parts not divisible by l. Let A ¯ l ( n) be the number of l -regular overpartitions of n. Andrews defined singular overpartitions … log into kindle account

Ranks of overpartitions modulo 4 and 8 Semantic Scholar

WebJun 1, 2004 · An overpartition is a partition in which the first occurrence of a number may be overlined. It has recently been shown [15, 16] that some of the classical techniques … WebRecall that $(a;q)_0:=1,\,(a;q)_n=(1-a)(1-aq)(1-aq^2)\cdots(1-aq^{n-1})$ and $(a;q)_{\infty}=(1-a)(1-aq)(1-aq^2)\cdots$. Let's introduce the following (generalized ... WebThe singular overpartition, Ck,i(n), counts the number of overpartitions of n in which no part is divisible by k and only parts ≡ ±i (mod k) may be overlined. For example, C3,1(4) = 10 with the relevant partitions being ... overpartitions.J. Number Theory,229:487–498,2024. [11] ... log into kindle cloud