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.
Description:
Bondarenko V. The classification of serial posets with the non-negative quadratic tits form being principal / V. Bondarenko , M .Styopochkina // Algebra and Discrete Mathematics. - 2019. - Vol. 27. - Number 2. - Рp.202 -211
