0387003 - MÚ 2013 RIV NL eng J - Článek v odborném periodiku
Brandts, J. - Dijkhuis, S. - de Haan, V. - Křížek, Michal
There are only two nonobtuse binary triangulations of the unit n-cube.
Computational Geometry-Theory and Applications. Roč. 46, č. 3 (2013), s. 286-297. ISSN 0925-7721. E-ISSN 1879-081X
Grant CEP: GA AV ČR(CZ) IAA100190803
Institucionální podpora: RVO:67985840
Klíčová slova: triangulation * simplexity * nonobtuse simplex
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.570, rok: 2013 ; AIS: 0.651, rok: 2013
Web výsledku:
http://www.sciencedirect.com/science/article/pii/S0925772112001150#DOI: https://doi.org/10.1016/j.comgeo.2012.09.005

Triangulations of the cube into a minimal number of simplices without additional vertices have been studied by several authors over the past decades. For 3≤n≤7 this so-called simplexity of the unit cube In is now known to be 5,16,67,308,1493, respectively. In this paper, we study triangulations of In with simplices that only have nonobtuse dihedral angles. A trivial example is the standard triangulation into n! simplices. In this paper we show that, surprisingly, for each n≥3 there is essentially only one other nonobtuse triangulation of In, and give its explicit construction. The number of nonobtuse simplices in this triangulation is equal to the smallest integer larger than n!(e-2).
Trvalý link: http://hdl.handle.net/11104/0217169