Geodesic
Homology of balanced complexes via the Fourier transform
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 4, pp. 565-571.

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Summary: Let $G _{0},\cdots , G _{ k }$ be finite abelian groups, and let $G _{0}\ast \dots \ast G _{ k }$ be the join of the 0-dimensional complexes $G _{ i }$. We give a characterization of the integral $k$-coboundaries of subcomplexes of $G _{0}\ast \dots \ast G _{ k }$ in terms of the Fourier transform on the group $G _{0}\times \dots \times G _{ k }$. 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: keywords simplicial homology, Fourier transform 
@article{JAC_2012__35_4_a4,
     author = {Meshulam, Roy},
     title = {Homology of balanced complexes via the {Fourier} transform},
     journal = {Journal of Algebraic Combinatorics},
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     publisher = {mathdoc},
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     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__35_4_a4/}
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Meshulam, Roy. Homology of balanced complexes via the Fourier transform. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 4, pp. 565-571. http://geodesic.mathdoc.fr/item/JAC_2012__35_4_a4/