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
Brazil
James A. Sellers
Department of Mathematics and Statistics
University of Minnesota, Duluth
Duluth, MN 55812
USA
Abstract:
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).
Full version: pdf,
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latex
(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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