2017
Том 69
№ 9

All Issues

Stepochkina M. V.

Articles: 2
Article (Russian)

Description of posets critical with respect to the nonnegativity of the quadratic Tits form

Bondarenko V. M., Stepochkina M. V.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

$(\min, \max)$-equivalence of posets and nonnegative Tits forms

Bondarenko V. M., Stepochkina M. V.

↓ Abstract   |   Full text (.pdf)

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.