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Congruence Modulo 4 for Andrews’ Even Parts Below Odd Parts Partition Function
We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of
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Andrews-Beck type congruences modulo powers of 5
Let NT ( m , k , n ) denote the total number of parts in the partitions of n with rank congruent to m modulo k . Andrews proved Beck’s conjecture on...
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Andrews–Beck Type Congruences Modulo 2 and 4 for Beck’s Partition Statistics
Recently, Andrews and Chern established a number of congruences modulo 5, 7, 11 and 13 on Beck’s partition statistics NT ( r , m , n ) and
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Finitely based congruence varieties
We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.
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Congruence relation between Stirling numbers of the first and second kinds
This paper consists of certain congruence properties of Stirling numbers of the first and second kinds. Some congruence relations between s ( n , k ) and S (...
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On cranks of partitions modulo 12 and 16
Let M ( t , m , n ) be the number of partitions of n with crank congruent to t modulo m . In this paper, we derive the generating functions of two...
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Congruences modulo powers of 2 for restricted partition triples due to Lin and Wang
In 2018, Lin and Wang introduced two restricted partition triples, whose generating functions are related to the reciprocals of Ramanujan–Gordon...
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Modulo 2 congruences for partitions with initial repetitions
Motivated by Andrews’ partitions with initial repetitions, we derive parity formulas for several functions for this class of partitions. In many...
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Deviation of the rank and crank modulo 11
In this paper, we build on the recent results of Frank Garvan and Rishabh Sarma as well as classical results of Bruce Berndt in order to establish...
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Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
In this paper, three parametric q -supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the...
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Some inequalities on cranks of cubic partitions modulo 4 and 6
A partition is a cubic partition if its even parts come in two colors. The crank for cubic partitions which explains cubic partition congruences...
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Growth of k-Dimensional Systoles in Congruence Coverings
We study growth of absolute and homological k -dimensional systoles of arithmetic n -manifolds along congruence coverings. Our main interest is in the...
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Infinitely many new properties of the congruence lattices of slim semimodular lattices
Slim planar semimodular lattices (SPS lattices or slim semimodular lattices for short) were introduced by G. Grätzer and E. Knapp in 2007. More than...
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Some missed congruences modulo powers of 2 for t-colored overpartitions
Recently, Nayaka and Naika (Bol Soc Mat Mex 28:66, 2022) proved several congruences modulo 16 and 32 for t -colored overpartitions with
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