Stepochkina M. V.
Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 611-624
We present the complete description of finite posets whose Tits form is not nonnegative but all proper subsets of which have nonnegative Tits forms. A similar result for positive forms was obtained by the authors earlier.
Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1157–1167
We study the relationship between the (min, max)-equivalence of posets and properties of their quadratic Tits form related to nonnegative definiteness. In particular, we prove that the Tits form of a poset S is nonnegative definite if and only if the Tits form of any poset $(\min, \max)$-equivalent to S is weakly nonnegative.