ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.)
ARS MATHEMATICA CONTEMPORANEA 23 (2023) #P1.04
https://doi.org/10.26493/1855-3974.2704.31a
(Also available at http://amc-journal.eu)
Finitizable set of reductions for polyhedral
quadrangulations of closed surfaces
Yusuke Suzuki *
Department of Mathematics, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku,
Niigata, 950-2181, Japan
Received 27 September 2021, accepted 19 March 2022, published online 22 September 2022
Abstract
In this paper, we discuss generating theorems of polyhedral quadrangulations of closed
surfaces. We prove that the set of the eight reductional operations {R1, . . . , R8} de-
fined for polyhedral quadrangulations is finitizable for any closed surface F 2, that is,
there exist finitely many minimal polyhedral quadrangulations of F 2 using such opera-
tions R1, . . . , R7 and R8. Furthermore, we show that any proper subset of {R1, . . . , R8}
is not finitizable for polyhedral quadrangulations of the torus.
Keywords: Generating theorem, reduction, finitizable set, polyhedral quadrangulation.
Math. Subj. Class. (2020): 05C10
*This work was supported by JSPS KAKENHI Grant Number 20K03714.
E-mail address: y-suzuki@math.sc.niigata-u.ac.jp (Yusuke Suzuki)
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/
ISSN 1855-3966 (tiskana izd.), ISSN 1855-3974 (elektronska izd.)
ARS MATHEMATICA CONTEMPORANEA 23 (2023) #P1.04
https://doi.org/10.26493/1855-3974.2704.31a
(Dostopno tudi na http://amc-journal.eu)
Dokončna množica redukcij poliedrskih
kvadrangulacij sklenjenih ploskev
Yusuke Suzuki *
Department of Mathematics, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku,
Niigata, 950-2181, Japan
Prejeto 27. septembra 2021, sprejeto 19. marca 2022, objavljeno na spletu 22. septembra 2022
Povzetek
V tem prispevku obravnavamo izreke v zvezi z generiranjem poliedrskih kvadrangulacij
sklenjenih ploskev. Dokažemo, da je množica osmih redukcijskih operacij {R1, . . . , R8},
definiranih za poliedrske kvadrangulacije, dokončna za katero koli sklenjeno ploskev F 2,
to pomeni, da obstaja končno mnogo minimalnih poliedrskih kvadrangulacij F 2, dobljenih
z uporabo teh operacij R1, . . . , R7 in R8. Pokažemo tudi, da nobena prava podmnožica
redukcijskih operacij {R1, . . . , R8}, definiranih za poliedrske kvadrangulacije torusa, ni
dokončna.
Ključne besede: Izrek o generiranju, redukcija, dokončna množica, poliedrska kvadrangulacija.
Math. Subj. Class. (2020): 05C10
*Ta raziskava je bila podprta s strani JSPS KAKENHI z dotacijo št. 20K03714.
E-poštni naslov: y-suzuki@math.sc.niigata-u.ac.jp (Yusuke Suzuki)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/