Vitalij M. Bondarenko, Marina V. Styopochkina, “On finite posets of $\pmb{inj}$-finite type and their Tits forms”, Algebra Discrete Math., 2006, no. 2, 17

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Algebra and Discrete Mathematics, 2006, Issue 2, Pages 17–21 (Mi adm253)

This article is cited in 9 scientific papers (total in 9 papers)

RESEARCH ARTICLE

On finite posets of $\pmb{inj}$-finite type and their Tits forms

Vitalij M. Bondarenko^a, Marina V. Styopochkina^b

^a Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, 01601 Kyiv, Ukraine
^b Kyiv Taras Shevchenko University, Volodymyrs'ka 64, Kyiv, 01033, Ukraine

Full-text PDF (203 kB) Citations (9)

Abstract: We prove one theorem on connection between $inj$-finiteness of a finite poset and positive definiteness of its Tits form.

Keywords: category of representations, $inj$-finite poset, positive definite form, the quadratic Tits form.

Received: 05.09.2006
Revised: 29.09.2006

Bibliographic databases:

Document Type: Article

MSC: 15A63, 16G20, 16G60

Language: English

Citation: Vitalij M. Bondarenko, Marina V. Styopochkina, “On finite posets of $\pmb{inj}$-finite type and their Tits forms”, Algebra Discrete Math., 2006, no. 2, 17–21

Citation in format AMSBIB

\Bibitem{BonSty06}

\by Vitalij~M.~Bondarenko, Marina~V.~Styopochkina

\paper On  finite posets of $\pmb{inj}$-finite type and their Tits forms

\jour Algebra Discrete Math.

\yr 2006

\issue 2

\pages 17--21

\mathnet{http://mi.mathnet.ru/adm253}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2320979}

\zmath{https://zbmath.org/?q=an:1164.16306}

Linking options:

https://www.mathnet.ru/eng/adm253

https://www.mathnet.ru/eng/adm/y2006/i2/p17

This publication is cited in the following 9 articles:

V. M. Bondarenko, M. Styopochkina, “On classifying the non-Tits $P$-critical posets”, Algebra Discrete Math., 32:2 (2021), 185–196
Vitalij M. Bondarenko, Marina V. Styopochkina, “The classification of serial posets with the non-negative quadratic Tits form being principal”, Algebra Discrete Math., 27:2 (2019), 202–211
Bondarenko V.M. Bortosh M.Yu., “Indecomposable and Isomorphic Objects in the Category of Monomial Matrices Over a Local Ring”, Ukr. Math. J., 69:7 (2017), 1034–1050
Gasiorek M. Simson D. Zajac K., “Structure and a Coxeter-Dynkin Type Classification of Corank Two Non-Negative Posets”, Linear Alg. Appl., 469 (2015), 76–113
Polak A., Simson D., “Coxeter Spectral Classification of Almost Tp-Critical One-Peak Posets Using Symbolic and Numeric Computations”, Linear Alg. Appl., 445 (2014), 223–255
Marcin Gąsiorek, Daniel Simson, Katarzyna Zając, “Algorithmic computation of principal posets using Maple and Python”, Algebra Discrete Math., 17:1 (2014), 33–69
Bocian R. Felisiak M. Simson D., “on Coxeter Type Classification of Loop-Free Edge-Bipartite Graphs and Matrix Morsifications”, 2013 15Th International Symposium on Symbolic and Numeric Algorithms For Scientific Computing (Synasc 2013), ed. Bjorner N. Negru V. Ida T. Jebelean T. Petcu D. Watt S. Zaharie D., IEEE, 2014, 115–118
Bondarenko V.M., Stepochkina M.V., “Description of Posets Critical with Respect to the Nonnegativity of the Quadratic Tits Form”, Ukr. Math. J., 61:5 (2009), 734–746
Bondarenko V.M., Stepochkina M.V., “(Min, Max)-Equivalence of Posets and Nonnegative Tits Forms”, Ukr. Math. J., 60:9 (2008), 1349–1359

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	278
References:	5
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