Kus, D and Singh, K and Venkatesh, R (2024) Identities of the multi-variate independence polynomials from heaps theory. In: Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 134 (1).
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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. © Indian Academy of Sciences 2024.
| Item Type: | Journal Article |
|---|---|
| Publication: | Proceedings of the Indian Academy of Sciences: Mathematical Sciences |
| Publisher: | Springer |
| Additional Information: | The copyright for this article belongs to Springer |
| Keywords: | Bijections; Bipartite subgraphs; Carty�foata monoids; Combinatorics; Commutative algebra; Heap; Independence polynomial of a graph; Independence polynomials; Inversion formulae; Monoids, Polynomials |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 29 Jul 2024 05:06 |
| Last Modified: | 29 Jul 2024 05:06 |
| URI: | http://eprints.iisc.ac.in/id/eprint/85180 |
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