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 $I$.
Keywords:
complete list positive tits sincere one peak posets provided applying combinatorial algorithms computer calculations using maple python problem whether square integer matrix mathbb mathbb mathbb congruent its transpose discussed affirmative answer given incidence matrices tits matrices widehat positive one peak posets nbsp
Affiliations des auteurs :
Marcin Gąsiorek
1
;
Daniel Simson
1
1
Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
Marcin Gąsiorek; Daniel Simson. A computation of positive one-peak posets that are Tits-sincere. Colloquium Mathematicum, Tome 127 (2012) no. 1, pp. 83-103. doi: 10.4064/cm127-1-6
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title = {A computation of positive one-peak posets that are {Tits-sincere}},
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