Orientations, lattice polytopes, and group arrangements II: Modular and integral flow Polynomials of graphs
Name
Stanley_Orientations lattice.pdf
Size
297.71 KB
Format
Adobe PDF
Checksum (MD5)
9cc47f4619fb21c819e92d04040ff5b1
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
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00373-011-1080-8
