Fundamental properties of Björner's complexes

Abstract

We study fundamental properties of Björner's complexes {Δn}n≥1. These simplicial complexes encode significant. The Prime Number Theorem and the Riemann Hypothesis are equivalent to certain estimates of the reduced Euler characteristics of these complexes as n→∞. In this paper, we show two facts: the dimension of Δn is approximated by log⁡n/log⁡log⁡n, and that the number of the maximal dimensional simplices in Δn is less than some constant to the dimension of Δn.