Conjectures for Cutting Pizza with Coxeter Arrangements

Richard Ehrenborg

doi:10.1080/10586458.2024.2379799

Conjectures for Cutting Pizza with Coxeter Arrangements

Richard Ehrenborg

Mathematics

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

Abstract

We are interested in conjecturing the sign of the pizza quantity (Formula presented.) for the irreducible Coxeter arrangements (Formula presented.) of type A_n, where (Formula presented.) or (Formula presented.), and type D_n, where n is odd. Our approach is to express the pizza quantity in terms of the pizza quantity of subarrangements known as 2-structures, and we obtain the first non-zero term in the multivariate Taylor expansion.

Original language	English
Journal	Experimental Mathematics
DOIs	https://doi.org/10.1080/10586458.2024.2379799
State	Accepted/In press - 2024

Bibliographical note

Publisher Copyright:
© 2024 Taylor & Francis Group, LLC.

Keywords

2-structures
coxeter arrangements
Pizza theorem
reflection groups

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1080/10586458.2024.2379799

Cite this

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abstract = "We are interested in conjecturing the sign of the pizza quantity (Formula presented.) for the irreducible Coxeter arrangements (Formula presented.) of type An, where (Formula presented.) or (Formula presented.), and type Dn, where n is odd. Our approach is to express the pizza quantity in terms of the pizza quantity of subarrangements known as 2-structures, and we obtain the first non-zero term in the multivariate Taylor expansion.",

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AB - We are interested in conjecturing the sign of the pizza quantity (Formula presented.) for the irreducible Coxeter arrangements (Formula presented.) of type An, where (Formula presented.) or (Formula presented.), and type Dn, where n is odd. Our approach is to express the pizza quantity in terms of the pizza quantity of subarrangements known as 2-structures, and we obtain the first non-zero term in the multivariate Taylor expansion.

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KW - reflection groups

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Conjectures for Cutting Pizza with Coxeter Arrangements

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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