An approach to the Herzog-Schönheim conjecture using automata
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866915024971235328 |
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| author | Chouraqui, Fabienne |
| author_facet | Chouraqui, Fabienne |
| contents | Let $G$ be a group and $H_1$,...,$H_s$ be subgroups of $G$ of indices $d_1$,...,$d_s$ respectively. In 1974, M. Herzog and J. Schönheim conjectured that if $\{H_iα_i\}_{i=1}^{i=s}$, $α_i\in G$, is a coset partition of $G$, then $d_1$,..,$d_s$ cannot be distinct. In this paper, we present a new approach to the Herzog-Schönheim conjecture based on automata and present a translation of the conjecture as a problem on automata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_03882 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | An approach to the Herzog-Schönheim conjecture using automata Chouraqui, Fabienne Group Theory Combinatorics Let $G$ be a group and $H_1$,...,$H_s$ be subgroups of $G$ of indices $d_1$,...,$d_s$ respectively. In 1974, M. Herzog and J. Schönheim conjectured that if $\{H_iα_i\}_{i=1}^{i=s}$, $α_i\in G$, is a coset partition of $G$, then $d_1$,..,$d_s$ cannot be distinct. In this paper, we present a new approach to the Herzog-Schönheim conjecture based on automata and present a translation of the conjecture as a problem on automata. |
| title | An approach to the Herzog-Schönheim conjecture using automata |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2001.03882 |