Deranged Matchings: Proofs and Conjectures

Daniel Johnston; P. Mark Kayll; Cory Palmer

doi:10.1080/00029890.2023.2274239

Deranged Matchings: Proofs and Conjectures

Daniel Johnston, P. Mark Kayll, Cory Palmer

Mathematical Sciences

Trinity College Hartford

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

Abstract

We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. Our tools blend combinatorics and analysis in a medley incorporating Inclusion-Exclusion and Tannery’s theorem.

Original language	English
Pages (from-to)	95-111
Number of pages	17
Journal	American Mathematical Monthly
Volume	131
Issue number	2
DOIs	https://doi.org/10.1080/00029890.2023.2274239
State	Published - 2024

Funding

Partially supported by Simons Foundation grants (#279367 to Mark Kayll & #712036 to Cory Palmer).

Funders	Funder number
Simons Foundation	279367, 712036

Keywords

05C70
40A05
Primary 05C30
Secondary 05A16

Access to Document

10.1080/00029890.2023.2274239

Cite this

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title = "Deranged Matchings: Proofs and Conjectures",

abstract = "We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. Our tools blend combinatorics and analysis in a medley incorporating Inclusion-Exclusion and Tannery{\textquoteright}s theorem.",

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author = "Daniel Johnston and Kayll, \{P. Mark\} and Cory Palmer",

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AU - Kayll, P. Mark

AU - Palmer, Cory

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AB - We introduce, and partially resolve, a conjecture that brings a three-centuries-old derangements phenomenon and its much younger two-decades-old analogue under the same umbrella. Our tools blend combinatorics and analysis in a medley incorporating Inclusion-Exclusion and Tannery’s theorem.

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KW - 40A05

KW - Primary 05C30

KW - Secondary 05A16

UR - https://www.scopus.com/pages/publications/85178404325

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DO - 10.1080/00029890.2023.2274239

M3 - Article

AN - SCOPUS:85178404325

SN - 0002-9890

VL - 131

SP - 95

EP - 111

JO - American Mathematical Monthly

JF - American Mathematical Monthly

IS - 2

ER -

Deranged Matchings: Proofs and Conjectures

Abstract

Funding

Keywords

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