Mircea Merca

Macmahon-type q-series

Abstract Motivated by earlier work of P. A. MacMahon and recent contributions of T. Amdeberhan, G. E. Andrews, K. Ono, A. Singh, and R. Tauraso on higher-order partition enumerants, we study a class of q -series arising from nested divisor structures. In particular, we consider t...

Signed Enumeration of Partitions with Exactly k Distinct Magnitudes of Odd Multiplicity

Abstract We introduce and study a family of q -series $$\{A_k(q)\}_{k\ge 0}$$ { A k ( q ) } k ≥ 0 arising from partitions whose distinct parts occur with odd multiplicities. Starting from their finite truncations $$A_{k,m}(q)$$ A k , m ( q ) , we derive several exact formulas exp...

The two-block odd partition function

Abstract We investigate arithmetic and combinatorial properties of the function a ( n ), which is the signed number of partitions of n into exactly two distinct part sizes, each occurring an odd number of times. We prove that $$a(n)\ge 0$$ a ( n ) ≥ 0 for all n , establishing a p...