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.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1157–1167, September, 2008.
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Bondarenko, V.M., Stepochkina, M.V. (Min, max)-equivalence of posets and nonnegative Tits forms. Ukr Math J 60, 1349–1359 (2008). https://doi.org/10.1007/s11253-009-0147-7
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DOI: https://doi.org/10.1007/s11253-009-0147-7