Zobrazeno 1 - 10
of 51
pro vyhledávání: '"11P84, 05A17"'
Autor:
Liu, Ji-Cai, Liu, Huan
Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2411.11815
Autor:
Fu, Shishuo, Li, Haijun
The number of sequences of odd length in strict partitions (denoted as $\mathrm{sol}$), which plays a pivotal role in the first paper of this series, is investigated in different contexts, both new and old. Namely, we first note a direct link between
Externí odkaz:
http://arxiv.org/abs/2410.16985
Autor:
Agarwal, Archit
Ramanujan recorded five $q$-series identities at the end of his second notebook and an unified generalization of these identities obtained by Bhoria, Eyyunni and Maji. Recently, Dixit and Patel gave a finite analogue of the identity of Bhoria et. al.
Externí odkaz:
http://arxiv.org/abs/2410.13430
The $(k,i)$-singular overpartitions, combinatorial objects introduced by Andrews in 2015, are known to satisfy Ramanujan-type congruences modulo any power of prime coprime to $6k$. In this paper we consider the parity of the number $\overline{C}_{k,i
Externí odkaz:
http://arxiv.org/abs/2312.01883
Autor:
Ballantine, Cristina, Welch, Amanda
PED partitions are partitions with even parts distinct while odd parts are unrestricted. Similarly, POD partitions have distinct odd parts while even parts are unrestricted. Merca proved several recurrence relations analytically for the number of PED
Externí odkaz:
http://arxiv.org/abs/2308.06123
Autor:
Ballantine, Cristina, Beck, George
The Fibonacci numbers are the prototypical example of a recursive sequence, but grow too quickly to enumerate sets of integer partitions. The same is true for the other classical sequences $a(n)$ defined by Fibonacci-like recursions: the tribonacci,
Externí odkaz:
http://arxiv.org/abs/2303.11493
Autor:
Ballantine, Cristina
We give combinatorial proofs of several recent results due to Merca on the sum of different parts congruent to $r$ modulo $m$ in all partitions of $n$. The proofs make use of some well known involutions from the literature and some new involutions in
Externí odkaz:
http://arxiv.org/abs/2303.06764
Autor:
Ballantine, Cristina, Folsom, Amanda
The celebrated Rogers-Ramanujan identities equate the number of integer partitions of $n$ ($n\in\mathbb N_0$) with parts congruent to $\pm 1 \pmod{5}$ (respectively $\pm 2 \pmod{5}$) and the number of partitions of $n$ with super-distinct parts (resp
Externí odkaz:
http://arxiv.org/abs/2303.03330
Autor:
Andrews, George E., Chern, Shane
Recently, $4$-regular partitions into distinct parts are connected with a family of overpartitions. In this paper, we provide a uniform extension of two relations due to Andrews for the two types of partitions. Such an extension is made possible with
Externí odkaz:
http://arxiv.org/abs/2301.11137
In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity
Externí odkaz:
http://arxiv.org/abs/2210.03457