The classification of serial posets with the non-negative quadratic tits form being principal

Abstract

Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets S satisfying the following conditions: (1) the quadratic Tits form qS(z) : Z

|S|+1 → Z of S is non-negative; (2) Ker qS(z) := {t| qS(t) = 0} is an infinite cyclic group (equivalently, the corank of the symmetric matrix of qS(z) is equal to 1); (3) for any m ∈ N, there is a poset S(m) ⊃ S such that S(m) satisfies (1), (2) and |S(m) \ S| = m.