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 $A\in {\mathbb M}_n({\mathbb Z})$ 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 $I$.
