Combinatorial proof of the minimal excludant theorem

DOI10.1142/S1793042121500615zbMath1494.11080arXiv1908.06789OpenAlexW3133811308MaRDI QIDQ3382985

Mircea Merca, Cristina M. Ballantine

Publication date: 23 September 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.06789

zbMATH Keywords

partitionsminimal excludantmex\(2\)-color partitionsleast gap in partition

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Elementary theory of partitions (11P81) Radix representation; digital problems (11A63)

Related Items (10)

Combinatorial perspectives on the Crank and mex partition statistics ⋮ A further look at cubic partitions ⋮ Minimal excludant over partitions into distinct parts ⋮ 4-regular partitions and the pod function ⋮ 6-regular partitions: new combinatorial properties, congruences, and linear inequalities ⋮ ON A CONJECTURE FOR A REFINEMENT OF THE SUM OF MINIMAL EXCLUDANTS ⋮ A refinement of a result of Andrews and Newman on the sum of minimal excludants ⋮ A new generalization of the minimal excludant arising from an analogue of Franklin's identity ⋮ A reversal of Schur's partition theorem ⋮ PED and POD partitions: combinatorial proofs of recurrence relations

Cites Work

• Unnamed Item
• The truncated pentagonal number theorem
• A truncated Jacobi triple product theorem
• Analysis of some new partition statistics
• Arithmetic properties of partitions with odd parts distinct
• Truncated theta series and a problem of Guo and Zeng
• Partitions and the minimal excludant
• Bisected theta series, least \(r\)-gaps in partitions, and polygonal numbers
• Overpartitions
• On identities of Watson type
• An Enumerative Proof of An Identity of Jacobi

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