Results 1 to 10 of about 40 (38)
New infinite families of congruences for Andrews’ (K, I)-singular overpartitions
Quaestiones Mathematicae, 2018 In a recent work, Andrews dened the singular overpartition functions, denoted by C̄k;i(n), which count the number of overpartitions of n in which no part is divisible by k and only parts ≡±i (mod k) may be overlined.
Olivia X M Yao
exaly +1 more source
Integer partitions into Diophantine pairs
Quaestiones Mathematicae, 2017 Let n, a and b be positive integers. The pair (a; b) is called an integer partition of n into Diophantine pair if n = a+b, ab+1 is a perfect square and a > b.
Bouroubi, S +4 more
exaly +1 more source
Counting certain quadratic partitions of zero modulo a prime number
Open Mathematics, 2021 Consider an odd prime number p≡2(mod3)p\equiv 2\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3). In this paper, the number of certain type of partitions of zero in Z/pZ{\mathbb{Z}}\hspace{-0.1em}\text{/}\hspace{-0.1em}p{\mathbb{Z}} is calculated using a ...
Xiao Wang, Li Aihua
doaj +1 more source
Ramanujan-type congruences modulo 4 for partitions into distinct parts
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the form Q(p⋅n+p2-124)≡0 (mod4),Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left(
Merca Mircea
doaj +1 more source
Some congruences for 3-component multipartitions
Open Mathematics, 2016 Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34).
Zhao Tao Yan, Jin Lily J., Gu C.
doaj +1 more source
Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
Open Mathematics, 2019 Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k and only parts ±i (mod k) may be overlined ...
Liu Eric H., Du Wenjing
doaj +1 more source
Parity results for broken 11-diamond partitions
Open Mathematics, 2019 Recently, Dai proved new infinite families of congruences modulo 2 for broken 11-diamond partition functions by using Hecke operators. In this note, we establish new parity results for broken 11-diamond partition functions.
Wu Yunjian
doaj +1 more source
A family of partitions with attached parts and 'N copies of N'
, 2015 in this paper we find two distinct combinatorial interpretations for a family of summations with several free parameters. In one case we used partitions with attached parts and in the other partitions with 'N copies of N'.
Mondek, P, Santos, JPO
core +1 more source
New congruences Modulo 5 and 9 for partitions with odd parts distinct
, 2021 Let pod(n) denote the number of partitions of an integer n wherein the odd parts are distinct. Recently, a number of congruences for pod(n) have been established.
Xue, Fanggang +2 more
core
Some consequences of an identity of B. Gordon
, 2004 unavailable at this time... Mathematics Subject Classification (2000): 11P83 Key words: Partitions into distinct parts, self-conjugate partitions, quintuple product identity Quaestiones Mathematicae 26(2003), 327 ...
Robbins, Neville
core