ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 52,57 Hachimori, Masahiro, University of Tokyo, Japan Non-constructible triangulations of balls In recent days shellability of simplicial complexes (and cell complexes) is extensively studied by many researchers of the area of combinatorics. Here we study a notion named constructibility, which is a notion weaker than shellability. In this talk we show an example of a non-constructible triangulation of a 3-ball, and present a way of testing constructibility under the condition that the given triangulation of a 3-ball has all of their vertices on the boundary. References: R. P. Stanley, Cohen-Macaulay rings and constructible polytopes, Bull. Amer. Math. Soc. 81 (1975), 133-135. G. M. Ziegler, Lectures on Polytopes, Springer-Verlag (1995), Chapter 8.