Mahonian partition identities via polyhedral geometry

Matthias Beck; Benjamin Braun; Nguyen Le

doi:10.1007/978-1-4614-4075-8_3

Mahonian partition identities via polyhedral geometry

Matthias Beck, Benjamin Braun, Nguyen Le

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

6 Scopus citations

Abstract

In a series of papers, George Andrews and various coauthors successfully revitalized seemingly forgotten, powerful machinery based on MacMahon's Ω operator to systematically compute generating functionsΣ_{λ{small element of}P} z^λ₁ 1. . . z^λ_nn for some set P of integer partitions λ = (λ₁,. . ., λ_n). Our goal is to geometrically prove and extend many of Andrews et al.'s theorems, by realizing a given family of partitions as the set of integer lattice points in a certain polyhedron.

Original language	English
Title of host publication	From Fourier Analysis and Number Theory to Radon Transforms and Geometry
Subtitle of host publication	In Memory of Leon Ehrenpreis
Editors	Hershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor
Pages	41-54
Number of pages	14
DOIs	https://doi.org/10.1007/978-1-4614-4075-8_3
State	Published - 2013

Publication series

Name	Developments in Mathematics
Volume	28
ISSN (Print)	1389-2177

Bibliographical note

Funding Information:
We thank Carla Savage for pointing out several results in the literature that were relevant to our project. This research was partially supported by the NSF through grants DMS-0810105 (Beck), DMS-0758321 (Braun), and DGE-0841164 (Le).

Funding

We thank Carla Savage for pointing out several results in the literature that were relevant to our project. This research was partially supported by the NSF through grants DMS-0810105 (Beck), DMS-0758321 (Braun), and DGE-0841164 (Le).

Funders	Funder number
National Science Foundation Arctic Social Science Program	DMS-0810105, DMS-0758321, DGE-0841164

Keywords

Composition
Integer lattice point
MacMahon'sωoperator
Partition identities
Polyhedral cone

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-1-4614-4075-8_3

Cite this

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title = "Mahonian partition identities via polyhedral geometry",

abstract = "In a series of papers, George Andrews and various coauthors successfully revitalized seemingly forgotten, powerful machinery based on MacMahon's Ω operator to systematically compute generating functionsΣλ\{small element of\}P zλ1 1. . . zλnn for some set P of integer partitions λ = (λ1,. . ., λn). Our goal is to geometrically prove and extend many of Andrews et al.'s theorems, by realizing a given family of partitions as the set of integer lattice points in a certain polyhedron.",

keywords = "Composition, Integer lattice point, MacMahon'sωoperator, Partition identities, Polyhedral cone",

author = "Matthias Beck and Benjamin Braun and Nguyen Le",

note = "Funding Information: We thank Carla Savage for pointing out several results in the literature that were relevant to our project. This research was partially supported by the NSF through grants DMS-0810105 (Beck), DMS-0758321 (Braun), and DGE-0841164 (Le). ",

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language = "English",

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Mahonian partition identities via polyhedral geometry. / Beck, Matthias; Braun, Benjamin; Le, Nguyen.
From Fourier Analysis and Number Theory to Radon Transforms and Geometry: In Memory of Leon Ehrenpreis. ed. / Hershel Farkas; Marvin Knopp; Robert Gunning; B.A Taylor. 2013. p. 41-54 (Developments in Mathematics; Vol. 28).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AU - Beck, Matthias

AU - Braun, Benjamin

AU - Le, Nguyen

N1 - Funding Information: We thank Carla Savage for pointing out several results in the literature that were relevant to our project. This research was partially supported by the NSF through grants DMS-0810105 (Beck), DMS-0758321 (Braun), and DGE-0841164 (Le).

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AB - In a series of papers, George Andrews and various coauthors successfully revitalized seemingly forgotten, powerful machinery based on MacMahon's Ω operator to systematically compute generating functionsΣλ{small element of}P zλ1 1. . . zλnn for some set P of integer partitions λ = (λ1,. . ., λn). Our goal is to geometrically prove and extend many of Andrews et al.'s theorems, by realizing a given family of partitions as the set of integer lattice points in a certain polyhedron.

KW - Composition

KW - Integer lattice point

KW - MacMahon'sωoperator

KW - Partition identities

KW - Polyhedral cone

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T3 - Developments in Mathematics

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BT - From Fourier Analysis and Number Theory to Radon Transforms and Geometry

A2 - Farkas, Hershel

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Mahonian partition identities via polyhedral geometry

Abstract

Publication series

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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