Classification of the posets of minmax types which are symmetric oversupercritical posets of the eighth order

V. M. Bondarenko, M. V. Styopochkina

Анотація


Класифікація частково впорядкованих множин, мінімаксним типом яких є симетричні надсуперкритичні частково впорядковані множини порядку 8

 

Наведено класифікацію частково впорядкованих множин, що тісно пов’язані (сто­совно своїх квадратичних форм Тітса) з узагальненнями критичних і суперкритичних частково впорядкованих множин, які вперше появилися у критеріях Клейнера та Назарової стосовно зображувальних типів частково впорядкованих множин. Ці критерії були першими в новій теорії зображень, започаткованій Л. О. Назаровою та А. В. Ройтером у 1972 р. Метод мінімаксного ізоморфізму (запроваджений першим автором) відіграє основну роль у поданому дослідженні.

 

Зразок для цитування: V. M. Bondarenko, M. V. Styopochkina, “Classification of the posets of minmax types which are symmetric oversupercritical posets of the eighth order,” Мат. методи та фіз.-мех. поля, 66, No. 1-2, 5–15 (2023), https://doi.org/10.15407/mmpmf2023.66.1-2.5-15


Ключові слова


діаграма Гассе, квадратична форма Тітса, критичні, надкритичні та супернадкритичні множини, мінімаксний тип, коефіцієнт транзитивності, вузловий елемент, щільна підмножина

Посилання


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