Journal of Integer Sequences, Vol. 23 (2020), Article 20.5.7

Parity Considerations for the Mex-Related Partition Functions of Andrews and Newman

Robson da Silva
Departamento de Ciência e Tecnologia
Universidade Federal de São Paulo
São José dos Campos, SP, 12247–014

James A. Sellers
Department of Mathematics and Statistics
University of Minnesota, Duluth
Duluth, MN 55812


In a recent paper, Andrews and Newman extended the mex-function to integer partitions and proved many partition identities connected with these functions. In this paper, we present parity considerations of one of the families of functions they studied, namely pt,t(n). Among our results, we provide complete parity characterizations of p1,1(n) and p3,3(n).

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(Concerned with sequences A002182 A004394 A040047 A323256 A323257.)

Received May 28 2020; revised version received June 5 2020. Published in Journal of Integer Sequences, June 5 2020.

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