10 citations · 17 across the 6 of their papers we have counts for
4 papers · 1 filter
A Partition Identity Related to Stanley's Theorem
Mircea Merca, Maxie D. Schmidt
In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of 's in the partitions of . A new expans…
-regular partitions: new combinatorial properties, congruences, and linear inequalities
Cristina Ballantine, Mircea Merca
We consider the number of the -regular partitions of , , and give infinite families of congruences modulo (in arithmetic progression) for . We also consid…
On Ramanujan-type Congruences for Multiplicative Functions
William Craig, Mircea Merca
The study of Ramanujan-type congruences for functions specific to additive number theory has a long and rich history. Motivated by recent connections between divisor sums and overp…
Inequalities involving the generating function for the number of partitions into odd parts
Cristina Ballantine, Mircea Merca
Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalitie…