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ON NEW MINIMAL EXCLUDANTS OF OVERPARTITIONS RELATED TO SOME q-SERIES OF RAMANUJAN

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  11 February 2025

ARITRAM DHAR Open the ORCID record for ARITRAM DHAR [Opens in a new window] ,
AVI MUKHOPADHYAY Open the ORCID record for AVI MUKHOPADHYAY [Opens in a new window]  and
RISHABH SARMA Open the ORCID record for RISHABH SARMA [Opens in a new window]
ARITRAM DHAR
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA e-mail: aritramdhar@ufl.edu
AVI MUKHOPADHYAY
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA e-mail: mukhopadhyay.avi@ufl.edu
RISHABH SARMA*
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
*
e-mail: rishabh.sarma@ufl.edu
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Abstract

Inspired by work of Andrews and Newman [‘Partitions and the minimal excludant’, Ann. Comb. 23 (2019), 249–254] on the minimal excludant or ‘mex’ of partitions, we define four new classes of minimal excludants for overpartitions and establish relations to certain functions due to Ramanujan.

Keywords

partitionsoverpartitionsminimal excludantmock theta functions

MSC classification

Primary: 05A15: Exact enumeration problems, generating functions
Secondary: 05A17: Partitions of integers 05A19: Combinatorial identities, bijective combinatorics 11P81: Elementary theory of partitions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 13
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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References

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