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Identities of the multi-variate independence polynomials from heaps theory

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Abstract

We study and derive identities for the multi-variate independence polynomials from the perspective of heaps theory. Using the inversion formula and the combinatorics of partially commutative algebras we show how the multi-variate version of Godsil type identity as well as the fundamental identity can be obtained from weight preserving bijections. Finally, we obtain a multi-variate identity involving connected bipartite subgraphs similar to the Christoffel–Darboux type identities obtained by Bencs.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Bochum, Universitätsstr. 150, Bochum, 44801, Germany

    Deniz Kus

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Kartik Singh

  3. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    R. Venkatesh

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  1. Deniz Kus
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  2. Kartik Singh
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  3. R. Venkatesh
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Correspondence to R. Venkatesh.

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Communicating Editor: C S Rajan

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Kus, D., Singh, K. & Venkatesh, R. Identities of the multi-variate independence polynomials from heaps theory. Proc Math Sci 134, 16 (2024). https://doi.org/10.1007/s12044-024-00786-2

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  • DOI: https://doi.org/10.1007/s12044-024-00786-2

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