| Title:
|
On chirality groups and regular coverings of regular oriented hypermaps (English) |
| Author:
|
Breda d'Azevedo, Antonio |
| Author:
|
Rodrigues, Ilda Inácio |
| Author:
|
Fernandes, Maria Elisa |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
1037-1047 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that if the Walsh bipartite map $\mathcal {M}=\mathcal {W}(\mathcal {H})$ of a regular oriented hypermap $\mathcal {H}$ is also orientably regular then both $\mathcal {M}$ and $\mathcal {H}$ have the same chirality group, the covering core of $\mathcal {M}$ (the smallest regular map covering $\mathcal {M}$) is the Walsh bipartite map of the covering core of $\mathcal {H}$ and the closure cover of $\mathcal {M}$ (the greatest regular map covered by $\mathcal {M}$) is the Walsh bipartite map of the closure cover of $\mathcal {H}$. We apply these results to the family of toroidal chiral hypermaps $(3,3,3)_{b,c}=\mathcal {W}^{-1}\{6,3\}_{b,c}$ induced by the family of toroidal bipartite maps $\{6,3\}_{b,c}$. (English) |
| Keyword:
|
hypermap |
| Keyword:
|
regular covering |
| Keyword:
|
chirality group |
| Keyword:
|
chirality index |
| Keyword:
|
toroidal hypermaps |
| MSC:
|
05C10 |
| MSC:
|
05C25 |
| MSC:
|
20B25 |
| MSC:
|
20F65 |
| MSC:
|
51E30 |
| MSC:
|
57M07 |
| MSC:
|
57M60 |
| idZBL:
|
Zbl 1249.05086 |
| idMR:
|
MR2886255 |
| DOI:
|
10.1007/s10587-011-0046-6 |
| . |
| Date available:
|
2011-12-16T15:45:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141805 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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