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A partition statistic for partitions with even parts distinct
Andrews, Hirschhorn, and Sellers studied the partition function ped ( n ) which enumerates the number of partitions of n with even parts distinct, and...
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On the combinatorics of the number of even parts in all partitions with distinct parts
Recently, Andrews and Merca obtained two identities concerning the number of even parts in all partitions of n into distinct parts. In this paper, we...
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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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Partitions into Distinct Parts Modulo Powers of 5
If pD(n) denotes the number of partitions of n into distinct parts, it is known that for α ≥ 1 and n ≥ 0,...
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A modular idealizer chain and unrefinability of partitions with repeated parts
Recently Aragona et al. have introduced a chain of normalizers in a Sylow 2-subgroup of Sym(2 n ), starting from an elementary abelian regular...
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On k-ary parts of maximal clones
The main problem of clone theory is to describe the clone lattice for a given basic set. For a two-element basic set this was resolved by E.L. Post,...
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Pointless Parts of Completely Regular Frames
(Completely regular) locales generalize (Tychonoff) spaces; indeed, the passage from a locale to its spatial sublocale is a well understood...
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Combinatorial proofs of two theorems related to the number of even parts in all partitions of n into distinct parts
Recently, Andrews and Merca considered the number of even parts in all partitions of n into distinct parts and obtained new combinatorial...
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Values at Positive Even Integer Points
The explicit formula for the values of the Riemann zeta-function \(\zeta (s)\)...
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Positive differences of overpartitions with separated parts
In this note, we investigate partition differences of overpartitions where overlined and non-overlined part are separated. As a consequence of our...
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Ramanujan’s Theta Functions and Parity of Parts and Cranks of Partitions
In this paper, we explore intricate connections between Ramanujan’s theta functions and a class of partition functions defined by the nature of the...
