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

Producción científica: Chapter › revisión exhaustiva

6 Citas (Scopus)

Resumen

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.

Idioma original	English
Título de la publicación alojada	From Fourier Analysis and Number Theory to Radon Transforms and Geometry
Subtítulo de la publicación alojada	In Memory of Leon Ehrenpreis
Editores	Hershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor
Páginas	41-54
Número de páginas	14
DOI	https://doi.org/10.1007/978-1-4614-4075-8_3
Estado	Published - 2013

Serie de la publicación

Nombre	Developments in Mathematics
Volumen	28
ISSN (versión impresa)	1389-2177

Nota bibliográfica

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).

Financiación

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).

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	DMS-0810105, DMS-0758321, DGE-0841164

ASJC Scopus subject areas

General Mathematics

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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). ",

year = "2013",

doi = "10.1007/978-1-4614-4075-8\_3",

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).

Producción científica: Chapter › revisión exhaustiva

TY - CHAP

T1 - Mahonian partition identities via polyhedral geometry

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).

PY - 2013

Y1 - 2013

N2 - 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.

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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UR - https://www.scopus.com/pages/publications/84880340218#tab=citedBy

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

M3 - Chapter

AN - SCOPUS:84880340218

SN - 9781461440741

T3 - Developments in Mathematics

SP - 41

EP - 54

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

A2 - Farkas, Hershel

A2 - Knopp, Marvin

A2 - Gunning, Robert

A2 - Taylor, B.A

ER -

Mahonian partition identities via polyhedral geometry

Resumen

Serie de la publicación

Nota bibliográfica

Financiación

ASJC Scopus subject areas

Acceder al documento

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Huella

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