A computation of positive one-peak posets that are Tits-sincere

Marcin Gąsiorek, and Daniel Simson. "A computation of positive one-peak posets that are Tits-sincere." Colloquium Mathematicae 127.1 (2012): 83-103. <http://eudml.org/doc/286171>.

@article{MarcinGąsiorek2012,
abstract = {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 $A ∈ ₙ(ℤ)$ is ℤ-congruent to its transpose $A^\{tr\}$ is also discussed. An affirmative answer is given for the incidence matrices $C_\{I\}$ and the Tits matrices $Ĉ_\{I\}$ of positive one-peak posets I.},
author = {Marcin Gąsiorek, Daniel Simson},
journal = {Colloquium Mathematicae},
keywords = {positive poset; Tits-sincere root; Coxeter polynomial; waist reflection; Tits bilinear form; Dynkin diagram; mesh translation quiver},
language = {eng},
number = {1},
pages = {83-103},
title = {A computation of positive one-peak posets that are Tits-sincere},
url = {http://eudml.org/doc/286171},
volume = {127},
year = {2012},
}

TY - JOUR
AU - Marcin Gąsiorek
AU - Daniel Simson
TI - A computation of positive one-peak posets that are Tits-sincere
JO - Colloquium Mathematicae
PY - 2012
VL - 127
IS - 1
SP - 83
EP - 103
AB - 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 $A ∈ ₙ(ℤ)$ is ℤ-congruent to its transpose $A^{tr}$ is also discussed. An affirmative answer is given for the incidence matrices $C_{I}$ and the Tits matrices $Ĉ_{I}$ of positive one-peak posets I.
LA - eng
KW - positive poset; Tits-sincere root; Coxeter polynomial; waist reflection; Tits bilinear form; Dynkin diagram; mesh translation quiver
UR - http://eudml.org/doc/286171
ER -