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Annals of Combinatorics, ISSN 0218-0006, 11/2014, Volume 18, Issue 4, pp. 709 - 722
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 11/2018, Volume 125, Issue 10, pp. 929 - 933
In this note, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of 1's in the partitions of... 
Secondary 11B75 | MSC: Primary 05A17 | MATHEMATICS
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 07/2019
Communications in Mathematical Physics (2019). https://doi.org/10.1007/s00220-019-03513-5 The class of minimal difference partitions MDP($q$) (with gap $q$) is... 
Journal Article
Aequationes mathematicae, ISSN 0001-9054, 6/2019, Volume 93, Issue 3, pp. 601 - 617
A composition of the positive integer n is a representation of n as an ordered sum of positive integers $$n=a_1+a_2+\dots +a_m.$$ n = a 1 + a 2 + ⋯ + a m .... 
11P81 | Partition | Composition | Analysis | Inversion | Mathematics | Combinatorics | 05A17 | Integers | Inversions
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 11/2017, Volume 33, Issue 11, pp. 1504 - 1512
Let b(n) denote the number of cubic partition pairs of n. In this paper, we aim to provide a strategy to obtain arithmetic properties of b(n). This gives... 
Mathematics, general | 11P83 | Mathematics | Cubic partition pair | congruence | 05A17 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical analysis | Partitions | Arithmetic
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 10/2019, Volume 126, Issue 9, pp. 859 - 859
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 8/2019, Volume 49, Issue 3, pp. 505 - 513
Recently, Andrews and Yee studied two-variable generalizations of two identities involving partition functions $$p_\omega (n)$$ p ω ( n ) and $$p_\nu (q)$$ p ν... 
11P81 | Fourier Analysis | Combinatorial proof | Functions of a Complex Variable | q -Series identity | Field Theory and Polynomials | 05A19 | Mathematics | Number Theory | Combinatorics | q -Binomial coefficient | 05A17 | q-Binomial coefficient | q-Series identity | MATHEMATICS | Mathematics - Combinatorics
Journal Article
Aequationes mathematicae, ISSN 0001-9054, 10/2017, Volume 91, Issue 5, pp. 859 - 869
This paper delves into the number of partitions of positive integers n into powers of 2 in which exactly m powers of 2 are used an odd number of times. The... 
Secondary 52B05 | 11P83 | Mathematics | Primary 05A17 | Combinatorics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Interdisciplinary Mathematics, ISSN 0972-0502, 11/2018, Volume 21, Issue 7-8, pp. 1533 - 1546
Let A ℓ (n) denote the number of bipartitions of n with ℓ-core. In this paper, we prove a theorem on congruences modulo 2 for A ℓ (n) with ℓ≥2 by employing a... 
ℓ-core | primary 11P83 | secondary 05A17 | Partition triples | Bipartitions | Congruences
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 12/2017, Volume 44, Issue 3, pp. 559 - 566
Let $$p_2(n)$$ p 2 ( n ) denote the number of cubic partitions. In this paper, we shall present two new congruences modulo 11 for $$p_2(n).$$ p 2 ( n ) . We... 
11P83 | Fourier Analysis | Cubic partition | Congruence | Functions of a Complex Variable | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | Recursion | 05A17 | MATHEMATICS
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 12/2019, Volume 79, Issue 2, pp. 227 - 235
Let $$\bar{p}(n)$$ p ¯ ( n ) denote the number of overpartitions of n. Recently, numerous congruences modulo powers of 2, 3 and 5 were established regarding... 
Overpartitions | 11P83 | Congruences | Theta functions | Mathematics, general | Mathematics | 05A17
Journal Article
Proceedings - Mathematical Sciences, ISSN 0253-4142, 6/2019, Volume 129, Issue 3, pp. 1 - 16
Congruences for partitions have received a great deal of attention in literature. Recently, Bringmann et al. (Electron J. Combin. 22(3) (2015) Paper 3.17, 16... 
Partition | 11P83 | Ramanujan-type congruence | Mathematics, general | Mathematics | overpartition | 05A17 | MATHEMATICS
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 6/2016, Volume 20, Issue 2, pp. 193 - 207
In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a... 
11P81 | ranks | positive moments | positivity | cranks | Mathematics | overpartitions | Combinatorics | 05A17 | SMALLEST PARTS | MATHEMATICS, APPLIED | NUMBER | INEQUALITIES | FROBENIUS REPRESENTATION | THEOREM | JACOBI FORMS | CONJUGATION | PARTITIONS | EVEN
Journal Article
Arabian Journal of Mathematics, ISSN 2193-5343, 06/2018, Volume 7, Issue 2, pp. 61 - 75
Abstract In this paper, we study various arithmetic properties of the function $$\overline{p}_{2,\,\, k}(n)$$ p¯2,k(n) , which denotes the number of $$(2,\,\,... 
05A15 | 11P83 | 05A17
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 6/2019, Volume 78, Issue 2, pp. 254 - 266
Let $$p_{k,3}(n)$$ p k , 3 ( n ) enumerate the number of 2-color partition triples of n where one of the colors appears only in parts that are multiples of k.... 
Partition | 11P83 | Congruences | Mathematics, general | Mathematics | 2-Color partition triples | 05A17 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 10/2019, Volume 113, Issue 4, pp. 355 - 366
The Nekrasov–Okounkov hook length formula provides a fundamental link between the theory of partitions and the coefficients of powers of the Dedekind eta... 
Polynomial | Partition | Secondary 05A19 | 11P82 | Mathematics, general | Mathematics | Primary 05A17 | Euler product | Hook formula | Unimodal | MATHEMATICS | Computer science
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2019, Volume 100, Issue 2, pp. 230 - 238
A strongly concave composition of is an integer partition with strictly decreasing and then increasing parts. In this paper we give a uniform asymptotic... 
primary 11P82 | 2010 Mathematics subject classification | secondary 05A16 | 05A17 | partitions | MATHEMATICS | asymptotics | concave composition | DYSONS CRANK | rank | ASYMPTOTIC FORMULAS
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 05/2019, Volume 126, Issue 5, pp. 418 - 429
At first glance, the multisets of positive integers that add to n, known as integer partitions, and Euler's number e do not have much in common. However, if... 
MSC: Primary 11P84 | Secondary 05A17 | MATHEMATICS | MSC
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 2/2017, Volume 42, Issue 2, pp. 301 - 323
Let $$\bar{p}(n)$$ p ¯ ( n ) denote the number of overpartitions of n. Fortin et al. and Hirschhorn and Sellers established some congruences modulo powers of 2... 
Overpartitions | 11P83 | Fourier Analysis | Congruences | Functions of a Complex Variable | Theta functions | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | 05A17 | FORMS | MATHEMATICS | ANALOGS | COEFFICIENTS | SQUARES | SUMS
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2019, Volume 100, Issue 1, pp. 41 - 47
A cyclotomic polynomial Phi(k)(x) is an essential cyclotomic factor of f(x) is an element of Z[x] if Phi(k)(x) vertical bar f(x) and every prime divisor of k... 
2010 Mathematics subject classification | primary 11R09 | secondary 05A17 | 12D05 | 12E05 | MATHEMATICS | cyclotomic polynomials | Newman polynomials | irreducible polynomials
Journal Article
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