Real Root Conjecture fails for five and higher dimensional spheres

Details Real Root Conjecture fails for five and higher dimensional spheres Real Root Conjecture fails for five and higher dimensional spheres

2005-01-04

arxiv.org/abs/math/0501046v1

Discrete & Computational Geometry, Vol. 34 (2005) Number 2, pp. 269-284

Mathematics

Combinatorics

15 pages, 1 figure

Scientific paper

10.1007/s00454-005-1171-5

A construction of convex flag triangulations of five and higher dimensional
spheres, whose h-polynomials fail to have only real roots, is given. We show
that there is no such example in dimensions lower than five.
A condition weaker than realrootedness is conjectured and some evidence is
provided

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