Finitizable set of reductions for polyhedral quadrangulations of closed surfaces - Suzuki, Yusuke (Ars mathematica contemporanea, 2023)
In this paper, we discuss generating theorems of polyhedral quadrangulations of closed surfaces. We prove that the set of the eight reductional operations ?$\{R_1, …, R_8\}$? defined 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 operations ?$R_1, …, R_7$? and ?$R_8$?. Furthermore, we show that any proper subset of ?$\{R_1, …, R_8\}$? is not finitizable for polyhedral quadrangulations of the torus.
Keywords: dokončna množica; finitizable set; generating theorem; izrek o generiranju; poliedrska kvadrangulacija; polyhedral quadrangulation; reduction; redukcija