Identities of the multi-variate independence polynomials from heaps theory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909617128210432 |
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| author | Kus, Deniz Singh, Kartik Venkatesh, R. |
| author_facet | Kus, Deniz Singh, Kartik Venkatesh, R. |
| contents | 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 new multi-variate identity involving connected bipartite subgraphs similar to the Christoffel-Darboux type identities obtained by Bencs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08029 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Identities of the multi-variate independence polynomials from heaps theory Kus, Deniz Singh, Kartik Venkatesh, R. Combinatorics 05E99, 05C25, 05C15, 20M32 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 new multi-variate identity involving connected bipartite subgraphs similar to the Christoffel-Darboux type identities obtained by Bencs. |
| title | Identities of the multi-variate independence polynomials from heaps theory |
| topic | Combinatorics 05E99, 05C25, 05C15, 20M32 |
| url | https://arxiv.org/abs/2209.08029 |