Diagonal Hooks and a Schmidt-Type Partition Identity

Shane Chern; Ae Ja Yee

doi:10.37236/10803

Diagonal Hooks and a Schmidt-Type Partition Identity

Shane Chern, Ae Ja Yee

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In a recent paper of Andrews and Paule, several Schmidt-type partition identities are considered within the framework of MacMahon’s Partition Analysis. Following their work, we derive a new Schmidt-type identity concerning diagonal hooks of partitions. We provide an analytic proof based on MacMahon’s Partition Analysis and a combinatorial proof through an involution on the set of partitions. We also establish connections between Schmidt-type distinct partitions and partitions with nonpositive and negative cranks.

Original language	English (US)
Article number	P2.10
Journal	Electronic Journal of Combinatorics
Volume	29
Issue number	2
DOIs	https://doi.org/10.37236/10803
State	Published - 2022

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/10803

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title = "Diagonal Hooks and a Schmidt-Type Partition Identity",

abstract = "In a recent paper of Andrews and Paule, several Schmidt-type partition identities are considered within the framework of MacMahon{\textquoteright}s Partition Analysis. Following their work, we derive a new Schmidt-type identity concerning diagonal hooks of partitions. We provide an analytic proof based on MacMahon{\textquoteright}s Partition Analysis and a combinatorial proof through an involution on the set of partitions. We also establish connections between Schmidt-type distinct partitions and partitions with nonpositive and negative cranks.",

author = "Shane Chern and Yee, {Ae Ja}",

note = "Funding Information: ∗Partially supported by a Killam Postdoctoral Fellowship from the Killam Trusts. †Partially supported by a grant (#633963) from the Simons Foundation. Publisher Copyright: {\textcopyright} The authors.",

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Diagonal Hooks and a Schmidt-Type Partition Identity

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