On properties of posets of MM-type (1, 2, 7)

V. M. Bondarenko, M. V. Styopochkina

Анотація


Обчислюємо коефіцієнт транзитивності для всіх частково впорядкованих множин ММ-типу (1, 2, 7) (тобто частково впорядкованих множин, які мінімаксно еквівалентні частково впорядкованій множині (1, 2, 7)).

 

Зразок для цитування: V. M. Bondarenko, M. V. Styopochkina, "On properties of posets of MM-type (1, 2, 7)," Прикл. проблеми механіки і математики, Вип. 17, 7–10 (2019), https://doi.org/10.15407/apmm2019.17.7-10


Ключові слова


1-надсуперкритична частково впорядкована множина, мiнiмаксна еквiвалентнiсть, коефiцiєнт транзитивностi, дiаграма Хассе, група автоморфiзмiв, MM-тип

Посилання


V. M. Bondarenko, "On (min, max)-equivalence of posets and applications to the Tits forms," Visn. Kyiv Univ., Ser. Fiz. Mat., No. 1, 24-25 (2005).

V. V. Bondarenko, V. M. Bondarenko, M. V. Stepochkina, I. V. Chervyakov, "1-over-supercritical partially ordered sets with trivial group of automorphisms and min-equivalence. I," Nauk. Visn. Uzhgorod. Univ., Ser. Mat. Inf., 22, No. 2, 17-25 (2011) (in Russian).

V. M. Bondarenko, A. M. Polishchuk, "On a criterion of positive definiteness for one class of infinite quadratic forms," Nelin. Kolyv., 6, No. 1, 3-14 (2003); English translation: Nonlinear Oscil., 6, No. 1, 1-12 (2003), https://doi.org/10.1023/A:1024886517654

V. M. Bondarenko, A. M. Polishchuk, "On finiteness of critical Tits forms of posets," Proc. Inst. Math. NAS Ukraine, 50, Part 3, 1061-1063 (2004).

V. M. Bondarenko, M. V. Styopochkina, "On posets of width two with positive Tits form," Algebra and Discrete Math., 4, No. 2, 20-35 (2005).

V. M. Bondarenko, M. V. Styopochkina, "(Min, max)-equivalence of posets and quadratic Tits form," in: Problems of Analysis and Algebra: Zb. Pr. Inst. Mat. NAN Ukr., 2, No. 3, 18-58 (2005) (in Russian).

V. M. Bondarenko, M. V. Styopochkina, "On finite posets of inj-finite type and their Tits forms," Algebra Discrete Math., 5, No. 2, 17-21 (2006).

V. M. Bondarenko, M. V. Stepochkina, "On serial posets with positive-definite quadratic Tits form," Nelin. Kolyv., 9, No. 3, 320-325 (2006); English translation: Nonlinear Oscil., 9, No. 3, 312-316 (2006), https://doi.org/10.1007/s11072-006-0045-y

V. M. Bondarenko, M. V. Stepochkina, "(Min, max)-equivalence of posets and non-negative Tits forms," Ukr. Mat. Zh., 60, No. 9, 1157-1167 (2008); English translation: Ukr. Math. J., 60, No. 9., 1349-1359 (2008), https://doi.org/10.1007/s11253-009-0147-7

V. M. Bondarenko, M. V. Stepochkina, "Description of posets critical with respect to the nonnegativity of the quadratic Tits form," Ukr. Mat. Zh., 61, No. 5, P. 611-624 (2009); English translation: Ukr. Math. J., 61, No. 5, 734-746 (2009), https://doi.org/10.1007/s11253-009-0245-6

V. M. Bondarenko, M. V. Styopochkina, "Coefficients of transitiveness of P-critical posets," in: Analysis and application: Zb. Pr. Inst. Mat. NAN Ukr., 14, No. 1, 46-51 (2017).

V. M. Bondarenko, M. V. Styopochkina, "On properties of posets of MM-type (1,3,5)," Nauk. Visn. Uzhgorod. Univ., Ser. Mat. Inf., 32, No. 1, 50-53 (2018).

Yu. A. Drozd, "Coxeter transformations and representations of partially ordered sets," Funkc. Anal. i Priložen., 8, No. 3, 34-42 (1974) (in Russian). https://doi.org/10.1007/BF01075695

P. Gabriel, "Unzerlegbare Darstellungen I," Manuscripta Math., 6, 71-103 (1972), https://doi.org/10.1007/BF01298413

L. A. Nazarova, A. V. Roiter, "Representations of posets," Zap. Nauch. Semin. LOMI, 28, 5-31 (1972) (in Russian).


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