Using Graph Theory to Derive Inequalities for the Bell Numbers
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914707658506240 |
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| author | Hertz, Alain Hertz, Anaelle Mélot, Hadrien |
| author_facet | Hertz, Alain Hertz, Anaelle Mélot, Hadrien |
| contents | The Bell numbers count the number of different ways to partition a set of $n$ elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph theory and integer sequences has motivated us to study properties on the average number of colors in the non-equivalent colorings of a graph to discover new non trivial inequalities for the Bell numbers. Example are given to illustrate our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_00552 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Using Graph Theory to Derive Inequalities for the Bell Numbers Hertz, Alain Hertz, Anaelle Mélot, Hadrien Discrete Mathematics Combinatorics The Bell numbers count the number of different ways to partition a set of $n$ elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph theory and integer sequences has motivated us to study properties on the average number of colors in the non-equivalent colorings of a graph to discover new non trivial inequalities for the Bell numbers. Example are given to illustrate our approach. |
| title | Using Graph Theory to Derive Inequalities for the Bell Numbers |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2104.00552 |