Results 1 to 10 of about 50 (48)

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
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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
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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.
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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
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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
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Ramanujan's Theta Functions and Parity of Parts and Cranks of Partitions. [PDF]

Ann Comb, 2023
Banerjee K, Dastidar MG.
europepmc   +1 more source

On sums of coefficients of polynomials related to the Borwein conjectures. [PDF]

Ramanujan J, 2022
Goswami A, Pantangi VRT.
europepmc   +1 more source

A single-variable proof of the omega SPT congruence family over powers of 5. [PDF]

Ramanujan J, 2023
Smoot NA.
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The Cause of Lead Poisoning in the Tinning of Metals. [PDF]

J Hyg (Lond), 1908
Duckering GE.
europepmc   +1 more source

Explaining unforeseen congruence relationships between PEND and POND partitions via an Atkin-Lehner involution. [PDF]

Ramanujan J
Sellers JA, Smoot NA.
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