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

Marcin Gąsiorek; Daniel Simson

Colloquium Mathematicae (2012)

- Volume: 127, Issue: 1, page 83-103
- ISSN: 0010-1354

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topMarcin 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 -

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