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Counting hypermaps by Egorychev’s method
Title Counting hypermaps by Egorychev’s method Author info Alexander Mednykh, Roman Nedela Author Mednykh Alexander 1953- (50%) UMBFP10 - Katedra matematiky
Co-authors Nedela Roman 1960- (50%) UMBFP10 - Katedra matematiky
Source document Analysis and Mathematical Physics. Vol. 6, no. 3 (2016), pp. 301-314. - Cham : Springer Nature Switzerland AG, 2016 Keywords Fuchsian groups hypermapy hypermaps matematika - mathematics Language English Country Germany systematics 51 Annotation © 2015, Springer Basel.The aim of this paper is to find explicit formulae for the number of rooted hypermaps with a given number of darts on an orientable surface of genus g≤ 3. Such formulae were obtained earlier for g= 0 and g= 1 by Walsh and Arquès respectively. We first employ the Egorychev’s method of counting combinatorial sums to obtain a new version of the Arquès formula for genus g= 1. Then we apply the same approach to get new results for genus g= 2 , 3. We could do it due to recent results by Giorgetti, Walsh, and Kazarian, Zograf who derived two different, but equivalent, forms of the generating functions for the number of hypermaps of genus two and three. Public work category ADC No. of Archival Copy 36932 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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