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Algebra and Discrete Mathematics, 2005, Issue 2, Pages 20–35 (Mi adm300)  

This article is cited in 18 scientific papers (total in 18 papers)

RESEARCH ARTICLE

On posets of width two with positive Tits form

Vitalij M. Bondarenkoa, Marina V. Styopochkinab

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
Abstract: We give a complete description of the finite posets of width two with the Tits form to be positive. This problem arises in studying the categories of representations of posets of finite type.
Keywords: minimax (semiminimax) sum, (min, max)-equivalent posets, positive form, the quadratic Tits form.
Received: 23.06.2005
Revised: 01.07.2005
Bibliographic databases:
Document Type: Article
MSC: 15A63, 16G20, 16G60
Language: English
Citation: Vitalij M. Bondarenko, Marina V. Styopochkina, “On posets of width two with positive Tits form”, Algebra Discrete Math., 2005, no. 2, 20–35
Citation in format AMSBIB
\Bibitem{BonSty05}
\by Vitalij~M.~Bondarenko, Marina~V.~Styopochkina
\paper On posets of width two with positive Tits form
\jour Algebra Discrete Math.
\yr 2005
\issue 2
\pages 20--35
\mathnet{http://mi.mathnet.ru/adm300}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2238215}
\zmath{https://zbmath.org/?q=an:1091.16007}
Linking options:
  • https://www.mathnet.ru/eng/adm300
  • https://www.mathnet.ru/eng/adm/y2005/i2/p20
  • This publication is cited in the following 18 articles:
    1. Gasiorek M., “a Coxeter Type Classification of One-Peak Principal Posets”, Linear Alg. Appl., 582 (2019), 197–217  crossref  mathscinet  zmath  isi  scopus
    2. 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  mathnet
    3. 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  mathnet  mathscinet
    4. 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  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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  crossref  mathscinet  zmath  isi  elib  scopus
    6. Bocian R., Felisiak M., Simson D., “Numeric and Mesh Algorithms for the Coxeter Spectral Study of Positive Edge-Bipartite Graphs and their Isotropy Groups”, J. Comput. Appl. Math., 259:B (2014), 815–827  crossref  mathscinet  zmath  isi  elib  scopus
    7. Marcin Gąsiorek, Daniel Simson, Katarzyna Zając, “Algorithmic computation of principal posets using Maple and Python”, Algebra Discrete Math., 17:1 (2014), 33–69  mathnet  mathscinet
    8. 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), eds. Bjorner N., Negru V., Ida T., Jebelean T., Petcu D., Watt S., Zaharie D., IEEE, 2014, 115–118  crossref  mathscinet  isi  scopus
    9. Polak A., Simson D., “Algorithmic Experiences in Coxeter Spectral Study of P-Critical Edge-Bipartite Graphs and Posets”, 2013 15Th International Symposium on Symbolic and Numeric Algorithms For Scientific Computing (Synasc 2013), eds. Bjorner N., Negru V., Ida T., Jebelean T., Petcu D., Watt S., Zaharie D., IEEE, 2014, 375–382  crossref  mathscinet  isi  scopus
    10. Mroz A., Zwara G., “Combinatorial Algorithms For Computing Degenerations of Modules of Finite Dimension”, Fundam. Inform., 132:4 (2014), 519–532  crossref  mathscinet  zmath  isi  elib  scopus
    11. Gasiorek M., Simson D., Zajac K., “on Corank Two Edge-Bipartite Graphs and Simply Extended Euclidean Diagrams”, 16Th International Symposium on Symbolic and Numeric Algorithms For Scientific Computing (Synasc 2014), eds. Winkler F., Negru V., Ida T., Jebelean T., Petcu D., Watt S., Zaharie D., IEEE Computer Soc, 2014, 66–73  crossref  isi  scopus
    12. Simson D., “Algorithms Determining Matrix Morsifications, Weyl Orbits, Coxeter Polynomials and Mesh Geometries of Roots for Dynkin Diagrams”, Fundam. Inform., 123:4 (2013), 447–490  crossref  mathscinet  zmath  isi  elib  scopus
    13. Gasiorek M., Simson D., “One-Peak Posets with Positive Quadratic Tits Form, their Mesh Translation Quivers of Roots, and Programming in Maple and Python”, Linear Alg. Appl., 436:7 (2012), 2240–2272  crossref  mathscinet  zmath  isi  scopus
    14. Gasiorek M., Simson D., “A Computation of Positive One-Peak Posets That Are Tits-Sincere”, Colloq. Math., 127:1 (2012), 83–103  crossref  mathscinet  zmath  isi  scopus
    15. Marczak G., Polak A., Simson D., “P-Critical Integral Quadratic Forms and Positive Unit Forms: an Algorithmic Approach”, Linear Alg. Appl., 433:11-12 (2010), 1873–1888  crossref  mathscinet  zmath  isi  scopus
    16. Simson D., “Integral Bilinear Forms, Coxeter Transformations and Coxeter Polynomials of Finite Posets”, Linear Alg. Appl., 433:4 (2010), 699–717  crossref  mathscinet  zmath  isi  elib  scopus
    17. 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  crossref  mathscinet  zmath  isi  elib  scopus
    18. Bondarenko V.M., Stepochkina M.V., “(Min, Max)-Equivalence of Posets and Nonnegative Tits Forms”, Ukr. Math. J., 60:9 (2008), 1349–1359  crossref  mathscinet  zmath  isi  elib  scopus
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