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Chromatic Polynomials of Simplicial Complexes

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Abstract

In this note we consider \(s\)-chromatic polynomials for finite simplicial complexes. When \(s=1\), the \(1\)-chromatic polynomial is just the usual graph chromatic polynomial of the \(1\)-skeleton. In general, the \(s\)-chromatic polynomial depends on the \(s\)-skeleton and its value at \(r\) is the number of \((r,s)\)-colorings of the simplicial complex.

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Notes

  1. The computations behind the examples of this note were carried out in the computer algebra system Magma [3].

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Acknowledgments

We thank Eric Babson whose questions, in November \(2011\) at the WATACBA workshop in Buenos Aires, led to this note.

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Authors and Affiliations

  1. Institut for Matematiske Fag, Københavns Universitet, Universitetsparken 5, 2100, Copenhagen, Denmark

    Jesper M. Møller

  2. KdV Instituut voor wiskunde, Universiteit van Amsterdam, Amsterdam, The Netherlands

    Gesche Nord

Authors
  1. Jesper M. Møller
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  2. Gesche Nord
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Corresponding author

Correspondence to Jesper M. Møller.

Additional information

The first author was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and by VILLUM FONDEN through the network for Experimental Mathematics in Number Theory, Operator Algebras, and Topology.

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Møller, J.M., Nord, G. Chromatic Polynomials of Simplicial Complexes. Graphs and Combinatorics 32, 745–772 (2016). https://doi.org/10.1007/s00373-015-1578-6

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