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 $I$.
@article{10_4064_cm127_1_6,
author = {Marcin G\k{a}siorek and Daniel Simson},
title = {A computation of positive one-peak posets that are {Tits-sincere}},
journal = {Colloquium Mathematicum},
pages = {83--103},
year = {2012},
volume = {127},
number = {1},
doi = {10.4064/cm127-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm127-1-6/}
}
TY - JOUR
AU - Marcin Gąsiorek
AU - Daniel Simson
TI - A computation of positive one-peak posets that are Tits-sincere
JO - Colloquium Mathematicum
PY - 2012
SP - 83
EP - 103
VL - 127
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm127-1-6/
DO - 10.4064/cm127-1-6
LA - en
ID - 10_4064_cm127_1_6
ER -
%0 Journal Article
%A Marcin Gąsiorek
%A Daniel Simson
%T A computation of positive one-peak posets that are Tits-sincere
%J Colloquium Mathematicum
%D 2012
%P 83-103
%V 127
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm127-1-6/
%R 10.4064/cm127-1-6
%G en
%F 10_4064_cm127_1_6
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
