On properties of posets of MM-type (1, 3, 4)

V. M. Bondarenko, M. V. Styopochkina

Анотація


Про властивості частково впорядкованих множин $MM$-типу (1, 3, 4)

Обчислено коефіцієнти транзитивності для всіх частково впорядкованих множин $MM$-типу (1, 3, 4) (тобто частково впорядкованих множин, які мінімаксно еквівалентні частково впорядкованій множині (1, 3, 4)).

 

Зразок для цитування: V. M. Bondarenko, M. V. Styopochkina, “On properties of posets of $MM$-type (1, 3, 4),” Прикл. проблеми механіки і математики, Вип. 20, 15–18 (2022), https://doi.org/10.15407/apmm2022.20.15-18

Ключові слова


сусідні елементи, коефіцієнт транзитивності, мінімаксна еквівалентність, антиізоморфізм, ММ-тип, висота ч.в. множини, вузловий елемент, щільна підмножина

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) (in Ukrainian).

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 (2006); Nonlin. 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,” in: Symmetry in Nonlinear Mathematical Physics, Vol. 50 of Proc. Inst. Math. NAS Ukraine, Part. 3, pp. 1061–1063 (2004).

V. M. Bondarenko, M. V. Styopochkina, “On posets of width two with positive Tits form,” Algebra 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. Nats. Akad. Nauk 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: Nonlin. Oscilat., 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 Nats. Akad. Nauk 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., 32, No. 1, 50–53 (2018).

V. M. Bondarenko, M. V. Stepochkina, M. V. Stoika, “The coefficients of transitiveness of the posets of MM-type being the smallest sypercritical poset of width 3,” Prykl. Probl. Mekh. Mat., No. 18, 11–13 (2020), https://doi.org/10.15407/apmm2020.18.11-13

V. M. Bondarenko, M. V. Stoika, M. V. Styopochkina, “The coefficients of transitivity of the posets of MM-type being the highest sypercritical poset,” Nauk. Visn. Uzhgorod. Univ., Ser. Mat., 40, No. 1, 11–18 (2022).

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