On combinatorial properties of minimal posets with nonnegative Tits quadratic form

Abstract

In this paper, we study combinatorial properties of finite posets connected with the negativity of their Tits quadratic form. We calculate the coefficients of transitivity for all minimal posets with nonnegative Tits quadratic form (such posets are called \(NP\)-critical and their number is 115 up to isomorphism and duality). Some relationships between these coefficients and the heights of posets are established.