The \((s,s+d,\dots,s+pd)\)-core partitions and the rational Motzkin paths

DOI10.1016/j.aam.2020.102096zbMath1456.05010arXiv2001.06651OpenAlexW3049372137MaRDI QIDQ2221764

Hyunsoo Cho, Jaebum Sohn, JiSun Huh

Publication date: 2 February 2021

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.06651

zbMATH Keywords

cornerssimultaneous core partitionsself-conjugategeneralized Dyck pathsrational Motzkin paths

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17)

Related Items (5)

Corners of self-conjugate \((s,s + 1)\)-cores and \(( \overline{s}, \overline{s + 1})\)-cores ⋮ Self-conjugate \(( s , s + d , s + 2 d )\)-core partitions and free Motzkin paths ⋮ Proof of a conjecture of Nath and Sellers on simultaneous core partitions ⋮ Combinatorics on bounded free Motzkin paths and its applications ⋮ Self-conjugate \((s,s+d,\dots ,s+pd)\)-core partitions and free Motzkin paths

Uses Software

• OEIS

Cites Work

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• Self-conjugate simultaneous \(p\)- and \(q\)-core partitions and blocks of \(A_n\)
• Partitions which are simultaneously \(t_1\)- and \(t_2\)-core
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• A bijection between ordinary partitions and self-conjugate partitions with same disparity
• On the enumeration of \((s, s + 1, s + 2)\)-core partitions
• Average size of a self-conjugate $(s,t)$-core partition
• The Corners of Core Partitions

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