Homology of balanced complexes via the Fourier transform

Roy Meshulam

doi:10.1007/s10801-011-0315-3

Homology of balanced complexes via the Fourier transform

Roy Meshulam

Mathematics

Technion - Israel Institute of Technology

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

Abstract

Let G0,⋯,Gk be finite abelian groups, and let G0 ^*⋯ ^* Gk be the join of the 0-dimensional complexes Gi. We give a characterization of the integral k-coboundaries of subcomplexes of G0 ^*⋯ ^* Gk in terms of the Fourier transform on the group G0 ×⋯ × Gk. This provides a short proof of an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.

Original language	English
Pages (from-to)	565-571
Number of pages	7
Journal	Journal of Algebraic Combinatorics
Volume	35
Issue number	4
DOIs	https://doi.org/10.1007/s10801-011-0315-3
State	Published - Jun 2012

Keywords

Fourier transform
Simplicial homology

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s10801-011-0315-3

Cite this

@article{5f23cf95cd644ad79959d94f394b4d2a,

title = "Homology of balanced complexes via the Fourier transform",

abstract = "Let G0,⋯,Gk be finite abelian groups, and let G0 *⋯ * Gk be the join of the 0-dimensional complexes Gi. We give a characterization of the integral k-coboundaries of subcomplexes of G0 *⋯ * Gk in terms of the Fourier transform on the group G0 ×⋯ × Gk. This provides a short proof of an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.",

keywords = "Fourier transform, Simplicial homology",

author = "Roy Meshulam",

note = "Funding Information: Acknowledgements Research supported by grants from the Israel Science Foundation and the U.S.— Israel Binational Science Foundation. The author would like to thank Vic Reiner for his helpful comments.",

year = "2012",

month = jun,

doi = "10.1007/s10801-011-0315-3",

language = "الإنجليزيّة",

volume = "35",

pages = "565--571",

journal = "Journal of Algebraic Combinatorics",

issn = "0925-9899",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - Homology of balanced complexes via the Fourier transform

AU - Meshulam, Roy

N1 - Funding Information: Acknowledgements Research supported by grants from the Israel Science Foundation and the U.S.— Israel Binational Science Foundation. The author would like to thank Vic Reiner for his helpful comments.

PY - 2012/6

Y1 - 2012/6

N2 - Let G0,⋯,Gk be finite abelian groups, and let G0 *⋯ * Gk be the join of the 0-dimensional complexes Gi. We give a characterization of the integral k-coboundaries of subcomplexes of G0 *⋯ * Gk in terms of the Fourier transform on the group G0 ×⋯ × Gk. This provides a short proof of an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.

AB - Let G0,⋯,Gk be finite abelian groups, and let G0 *⋯ * Gk be the join of the 0-dimensional complexes Gi. We give a characterization of the integral k-coboundaries of subcomplexes of G0 *⋯ * Gk in terms of the Fourier transform on the group G0 ×⋯ × Gk. This provides a short proof of an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.

KW - Fourier transform

KW - Simplicial homology

UR - http://www.scopus.com/inward/record.url?scp=84863726061&partnerID=8YFLogxK

U2 - 10.1007/s10801-011-0315-3

DO - 10.1007/s10801-011-0315-3

M3 - مقالة

SN - 0925-9899

VL - 35

SP - 565

EP - 571

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 4

ER -

Homology of balanced complexes via the Fourier transform

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this