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 q ˆ I : Z I → 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 A n , n ⩾ 1 , three infinite series of type D n , n ⩾ 4 , and a finite set of 193 posets of the Coxeter-Dynkin types E 6 , E 7 , and E 8 . For each such a poset I of the Coxeter-Dynkin type Δ, a Z -bilinear equivalence of the bilinear form b I of I with the Euler bilinear form b Δ of the Dynkin diagram Δ is presented by computing a Z -invertible matrix B defining the equivalence.