A computation of positive one-peak posets that are Tits-sincere
Tom 127 / 2012
Colloquium Mathematicum 127 (2012), 83-103
MSC: Primary 06A11, 16G20; Secondary 06A07, 05C50, 15A63.
DOI: 10.4064/cm127-1-6
Streszczenie
A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix is {\mathbb Z}-congruent to its transpose A^{\rm tr} is also discussed. An affirmative answer is given for the incidence matrices C_I and the Tits matrices \widehat C\!\!_I of positive one-peak posets I.
