Mircea Merca

activity

20142023

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3 papers · 1 filter

math.NT2023★ 10 cited

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 $1$ 's in the partitions of $n$ . A new expans…

math.CO2023★ 7 cited

The partition function $p (n)$ in terms of the classical Möbius function

Mircea Merca, Maxie D. Schmidt

In this paper, we investigate decompositions of the partition function $p (n)$ from the additive theory of partitions considering the famous Möbius function $μ (n)$ from multiplicati…

math.NT2023

$6$ -regular partitions: new combinatorial properties, congruences, and linear inequalities

Cristina Ballantine, Mircea Merca

We consider the number of the $6$ -regular partitions of $n$ , $b_{6} (n)$ , and give infinite families of congruences modulo $3$ (in arithmetic progression) for $b_{6} (n)$ . We also consid…

A Partition Identity Related to Stanley's Theorem

The partition function p(n) in terms of the classical Möbius function

6-regular partitions: new combinatorial properties, congruences, and linear inequalities

The partition function $p (n)$ in terms of the classical Möbius function

$6$ -regular partitions: new combinatorial properties, congruences, and linear inequalities