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On the monotone upper bound problem

Autor
Pfeifle, J.; Ziegler, G. M.
Tipus d'activitat
Article en revista
Revista
Experimental mathematics
Data de publicació
2004
Volum
13
Número
1
Pàgina inicial
1
Pàgina final
11
Repositori
http://hdl.handle.net/2117/7737 Obrir en finestra nova
Resum
The Monotone Upper Bound Problem asks for the maximal number M(d,n) of vertices on a strictly-increasing edge-path on a simple d-polytope with n facets. More specifically, it asks whether the upper bound M(d,n) ≤ Mubt(d,n) provided by McMullen’s (1970) Upper Bound Theorem is tight, where Mubt(d,n) is the number of vertices of a dual-to-cyclic d-polytope with n facets. It was recently shown that the upper bound M(d,n) ≤ Mubt(d,n) holds with equality for small dimensions (d ≤ 4: Pfeifle, 2...
Citació
Pfeifle, J.; Ziegler, G. M. On the monotone upper bound problem. "Experimental mathematics", 2004, vol. 13, núm. 1, p. 1-11.
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants

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