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Algebra Discrete Math., 2016, Volume 22, Issue 2, Pages 240–261 (Mi adm586)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

A horizontal mesh algorithm for posets with positive Tits form

Mariusz Kaniecki, Justyna Kosakowska, Piotr Malicki, Grzegorz Marczak

Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

Abstract: Following our paper [Fund. Inform. 136 (2015), 345–379], we define a horizontal mesh algorithm that constructs a $\widehat{\Phi}_I$-mesh translation quiver $\Gamma(\widehat{\mathcal{R}}_I,\widehat{\Phi}_I)$ consisting of $\widehat{\Phi}_I$-orbits of the finite set $\widehat{\mathcal{R}}_I=\{v\in\mathbb{Z}^I\; ;\;\widehat{q}_I(v)=1\}$ of Tits roots of a poset $I$ with positive definite Tits quadratic form $\widehat q_I:\mathbb{Z}^I \to \mathbb{Z}$. Under the assumption that $\widehat q_I:\mathbb{Z}^I \to \mathbb{Z}$ is positive definite, the algorithm constructs $\Gamma(\widehat{\mathcal{R}}_I,\widehat{\Phi}_I)$ such that it is isomorphic with the $\widehat{\Phi}_D$-mesh translation quiver $\Gamma({\mathcal{R}}_D,{\Phi}_D)$ of $\widehat{\Phi}_D$-orbits of the finite set ${\mathcal{R}}_D$ of roots of a simply laced Dynkin quiver $D$ associated with $I$.

Keywords: poset, combinatorial algorithm, Dynkin diagram, mesh geometry of roots, quadratic form.

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Bibliographic databases:
MSC: 68R10, 05C50, 06A07, 15A63
Received: 22.12.2015
Revised: 05.01.2016
Language:

Citation: Mariusz Kaniecki, Justyna Kosakowska, Piotr Malicki, Grzegorz Marczak, “A horizontal mesh algorithm for posets with positive Tits form”, Algebra Discrete Math., 22:2 (2016), 240–261

Citation in format AMSBIB
\Bibitem{KanKosMal16}
\by Mariusz~Kaniecki, Justyna~Kosakowska, Piotr~Malicki, Grzegorz~Marczak
\paper A~horizontal mesh algorithm for posets with~positive Tits form
\jour Algebra Discrete Math.
\yr 2016
\vol 22
\issue 2
\pages 240--261
\mathnet{http://mi.mathnet.ru/adm586}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3593123}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000392709600007}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. Simson, K. Zajac, “Inflation algorithm for loop-free non-negative edge-bipartite graphs of corank at least two”, Linear Alg. Appl., 524 (2017), 109–152  crossref  mathscinet  zmath  isi  scopus
    2. B. Makuracki, D. Simson, B. Zyglarski, “Inflation agorithm for Cox-regular postive edge-bipartite graphs with loops”, Fundam. Inform., 153:4 (2017), 367–398  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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