Orientations, lattice polytopes, and group arrangements II: Modular and integral flow Polynomials of graphs
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Stanley_Orientations lattice.pdf
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Author(s) •
Chen, Beifang
Stanley, Richard P.
Date Issued
August 2011
Journal
Graphs and Combinatorics
Publisher
Springer-Verlag
Citation
Chen, Beifang, and Richard P. Stanley. “Orientations, Lattice Polytopes, and Group Arrangements II: Modular and Integral Flow Polynomials of Graphs.” Graphs and Combinatorics (2011).
Version
Author's final manuscript
Abstract
We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory of Ehrhart polynomials to obtain properties of modular and integral flow polynomials. The emphasis is on the geometrical treatment through subgroup arrangements and Ehrhart polynomials. Such viewpoint leads to a reciprocity law on the modular flow polynomial, which gives rise to an interpretation on the values of the modular flow polynomial at negative integers and answers a question by Beck and Zaslavsky.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00373-011-1080-8