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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 5, pp. 611–624, May, 2009.
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Bondarenko, V.M., Stepochkina, M.V. Description of posets critical with respect to the nonnegativity of the quadratic Tits form. Ukr Math J 61, 734–746 (2009). https://doi.org/10.1007/s11253-009-0245-6
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DOI: https://doi.org/10.1007/s11253-009-0245-6