39 citations · 43 across the 10 of their papers we have counts for
7 papers · 1 filter
The powers of two as sums over partitions
Mircea Merca
In this paper, we investigate two methods to express the natural powers of as sums over integer partitions. First we consider a formula by N. J. Fine that allows us to express…
On a nonlinear relation for computing the overpartition function
Mircea Merca
In 1939, H. S. Zuckerman provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the overpartition function .…
-Series congruences involving statistical mechanics partition functions in regime III and IV of Baxter's solution of the hard-hexagon model
Mircea Merca
For each , the generating function of , the number of partitions of into odd parts or congruent to , , arises naturally in regime III o…
Combinatorial Proof of the Minimal Excludant Theorem
Cristina Ballantine, Mircea Merca
The minimal excludant of a partition , , is the smallest positive integer that is not a part of . For a positive integer , denotes the sum…
A convolution for the complete and elementary symmetric functions
Mircea Merca
In this paper we give a convolution identity for the complete and elementary symmetric functions. This result can be used to proving and discovering some combinatorial identities i…
Factorization Theorems for Generalized Lambert Series and Applications
Mircea Merca, Maxie D. Schmidt
We prove new variants of the Lambert series factorization theorems studied by Merca and Schmidt (2017) which correspond to a more general class of Lambert series expansions of the…