Programming in PYTHON and an algorithmic description of positive wandering on one-peak posets

Algorithms that compute all finite posets I with a unique maximal element such that the Tits quadratic form qˆI:ZI→Z is positive definite are presented. They also determine the Coxeter-Dynkin types of such posets. It is shown that there is one infinite series of the Coxeter-Dynkin type An,n⩾1, three infinite series of type Dn,n⩾4, and a finite set of 193 posets of the Coxeter-Dynkin types E6,E7, and E8. For each such a poset I of the Coxeter-Dynkin type Δ, a Z-bilinear equivalence of the bilinear form bI of I with the Euler bilinear form bΔ of the Dynkin diagram Δ is presented by computing a Z-invertible matrix B defining the equivalence.