A new generalization of the minimal excludant arising from an analogue of Franklin's identity

DOI10.1016/j.disc.2023.113334OpenAlexW4320169615MaRDI QIDQ2689507

Pramod Eyyunni, Bibekananda Maji, Subhash Chand Bhoria

Publication date: 10 March 2023

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.03658

zbMATH Keywords

partition identitiesEuler's identityFranklin's identitymex\(r\)-chain mex

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81)

Uses Software

• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis of some new partition statistics
• Combinatorial proofs and generalizations of conjectures related to Euler's partition theorem
• Partitions and the minimal excludant
• Beck-type companion identities for Franklin's identity via a modular refinement
• Partitions and the maximal excludant
• Combinatorial perspectives on the Crank and mex partition statistics
• Bisected theta series, least \(r\)-gaps in partitions, and polygonal numbers
• Dyson's crank and the mex of integer partitions
• On the number of even parts in all partitions of \(n\) into distinct parts
• Combinatorial proof of the minimal excludant theorem
• Euler’s Partition Theorem and Refinements Without Appeal to Infinite Products
• Minimal excludant over partitions into distinct parts
• Parity Considerations for Mex-Related Partition Functions of Andrews and Newman

This page was built for publication: A new generalization of the minimal excludant arising from an analogue of Franklin's identity