Congruences for (2, 3)-regular partition with designated summands

Let $PD_{2, 3}(n)$ count the number of partitions of $n$ with designated summands in which parts are not multiples of $2$ or $3$. In this work, we establish congruences modulo powers of 2 and 3 for $PD_{2, 3}(n)$. For example, for each \quad $n\ge0$ and $\alpha\geq0$ \quad $PD_{2, 3}(6\cdot4^{\alpha+2}n+5\cdot4^{\alpha+2})\equiv 0 \pmod{2^4}$ and $PD_{2, 3}(4\cdot3^{\alpha+3}n+10\cdot3^{\alpha+2})\equiv 0 \pmod{3}.

Andrews� singular overpartitions with odd parts

Recently singular overpartitions was defined and studied by G. E. Andrews. He showed that such partitions can be enumerated by Cδ,i(n), the number of overpartitions of n such that no part is divisible by δ and only parts � ±i (mod δ) may be overlined. In this paper, we establish several infinite families of congruences COδ,i(n), the number of singular overpartitions of n into odd parts such that no part is divisible by δ and only parts � ±i (mod δ) may be overlined. For example, for all n � 0 and α � 0, CO3,1(4·3α+3n+7·3α+2) � 0 (mod 8). © 2017, Adam Mickiewicz University Press. All rights reserved

Congruences for -regular cubic partition pairs

Abstract Let b(n) denote the number of -regular cubic partition pairs of n. In this paper, we establish some infinite families of congruences of modulo 27 and 81 for b(n). For example, for each α ≥ 0 and n ≥ 1, b9 3α+4n + 3α+4 − 2 ≡ 0 (mod 27), b9 (27n + 25) ≡ 0 (mod 81)

Arithmetic properties of 3-regular bi-partitions with designated summands

Recently Andrews, Lewis and Lovejoy introduced the partition functions PD(n) defined by the number of partitions of n with designated summands and they found several modulo 3 and 4. In this paper, we find several congruences modulo 3 and 4 for PBD3(n), which represent the number of 3-regular bi-partitions of n with designated summands. For example, for each n � 1 and α � 0 PBD3(4 · 3α+2n + 10 · 3α+1) � 0 (mod 3). © 2017, Drustvo Matematicara Srbije. All rights reserved

Congruences for Partition Quadruples with t-Cores

Let Ct(n) denote the number of partition quadruples of n with t-cores for t = 3,5,7,25. We establish some Ramanujan type congruences modulo 5, 7, 8 for Ct(n). For example, n ≥ 0, we haveC5(5n+4)=0(mod5),C7(7n+6)=0(mod7),C3(16n+14)=0(mod8).\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document} \begin{array}{@{}rcl@{}} C_{5}(5n+4)&\equiv& 0\pmod{5},\\ C_{7}(7n+6)&\equiv& 0\pmod{7},\\ C_{3}(16n+14)&\equiv& 0\pmod{8}. \end{array} \end{document} Citation Statements: 0 0 0 0 Making Science Reliable 0 0 0 0 Citing Publications Supporting Mentioning Contrasting View Citations See all citations for this article at scite.ai scite is a platform that combines deep learning with expert analysis to automatically classify citations as supporting, contrasting or mentioning. Find In LibraryFull Tex

Some New Congruences for Andrews' Singular Overpartition Pairs

In a recent work, Andrews defined the combinatorial objects called singular over partitions denoted by C¯k,i(n), which count the number of over partitions of n in which no part is divisible by k and only parts congruent to ± i modulo k may be overlined. Many authors have found congruences and infinite families of congruences modulo powers of 2 and 3. In this paper, we find some new infinite families of congruences for C¯1,26(n) modulo 27 and congruences modulo 4 for C¯1,512(n), C¯3,39(n) and C¯5,515(n)

Innite Families of Congruences for 2-Color overpartitions

[[abstract]]Let p_3(n) denote the number of overpartitions of n with 2-color in which one of the colors appears only in parts that are multiples of 3. In this work, we establish several infinite families of congruences modulo powers of 2 and 3 for p_3(n). We also show that for each n ≥ 0 and α ≥ 0, p_3(6．5^(2α+4) n+(30i+25)5^(2α+2))≡0 (mod 18), where i = 1, 2, 3, 4