Genus of the cartesian product of triangles

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F15%3A00087405" target="_blank" >RIV/00216224:14330/15:00087405 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Genus of the cartesian product of triangles
Original language description
We investigate the orientable genus of G(n), the cartesian product of n triangles, with a particular attention paid to the two smallest unsolved cases n = 4 and 5. Using a lifting method we present a general construction of a low -genus embedding of G(n)using a low-genus embedding of G(n-1). Combining this method with a computer search and a careful analysis of face structure we show that 30 <= gamma (G(4)) <= 37 and 133 <= gamma(G(5)) <= 190. Moreover, our computer search resulted in morethan 1300 non isomorphic minimum -genus embeddings of G(3). We also introduce genus range of a group and (strong) symmetric genus range of a Cayley graph and of a group. The (strong) symmetric genus range of irredundant Cayley graphs of Z(p)(n) is calculated for all odd primes p.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/EE2.3.30.0009" target="_blank" >EE2.3.30.0009: Employment of Newly Graduated Doctors of Science for Scientific Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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