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Reflexible maps and hypermaps with face–stabilisers pointwise stabilising half the faces
| Content Provider | Semantic Scholar |
|---|---|
| Author | D'Azevedo, Antonio Breda |
| Copyright Year | 2002 |
| Abstract | This paper deals mainly with reflexible hypermaps in which the stabiliser of a hyperface fixes exactly half the hyperfaces - these reflexible hypermaps are called here 2-dichromatic. The number \(F({\cal H})\) of hyperfaces of any 2-dichromatic hypermap \( \cal H \) must be necessarily even and greater than or equal to 4. We prove that if \( F({\cal H})=2n>4 \) then \( \cal H \) is necessarily orientable and of type \( (4a,4b,{nc\over 2}) \), for some positive integers \( a \), \( b \) and \( c \), and show that the automorphism group of a 2-dichromatic hypermap is a wreath product. We also construct an infinite family of orientable 2-dichromatic hypermaps of type \( (4,4,{n\over 2}) \) with 2n hyperfaces (n even). If \( \cal M \) is a 2-dichromatic map then \( F({\cal M})=4 \). In 1959 Sherk [19] described an infinite family of orientable maps, he denoted by \( \{j\cdot p,q\} \), where \( j \), \( p \) and \( q \) are positive integers satisfying certain conditions. We find in the dual family \( \{q,j\cdot p\} \) a subfamily of infinitely many 2-dichromatic maps. |
| Starting Page | 93 |
| Ending Page | 111 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00022-002-8586-4 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s00022-002-8586-4 |
| Alternate Webpage(s) | https://doi.org/10.1007/s00022-002-8586-4 |
| Volume Number | 73 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
