On the Tutte–Krushkal–Renardy polynomial for cell complexes
| Autor: | Carlos Bajo, Sergei Chmutov, Bradley Lewis Burdick |
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| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
HOMFLY polynomial Alternating polynomial Bracket polynomial Chromatic polynomial Theoretical Computer Science Matrix polynomial Combinatorics Reciprocal polynomial Computational Theory and Mathematics Stable polynomial Discrete Mathematics and Combinatorics Monic polynomial Mathematics |
| Zdroj: | Journal of Combinatorial Theory, Series A. 123:186-201 |
| ISSN: | 0097-3165 |
| DOI: | 10.1016/j.jcta.2013.12.006 |
| Popis: | Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte-Krushkal-Renardy polynomial evaluated at the origin gives a weighted count of cellular spanning trees, and therefore its free term can be calculated by the cellular matrix-tree theorem of Duval et al. In the case of cell decompositions of a sphere, this modified polynomial satisfies the same duality identity as the original polynomial. We find that evaluating the Tutte-Krushkal-Renardy along a certain line gives the Bott polynomial. Finally we prove skein relations for the Tutte-Krushkal-Renardy polynomial. |
| Databáze: | OpenAIRE |
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