Funcrional and analytic representations of the total permutation

Pichugina, Oksana; Яковлев, Сергей Всеволодович

doi:10.15587/1729-4061.2016.58550

Cited by 13 publications

(1 citation statement)

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“…For vertex-located combinatorial point configurations, the theory of convex extensions of functions is developed [83,84,90,91], and the current state is covered in the publications [18,40,48,49,98,105]. General approaches to continuous functional representation of various classes of combinatorial point configurations are presented in [39][40][41][48][49][50].…”

Section: Combinatorically Equivalent Partial Multipermutohedramentioning

confidence: 99%

Combinatorial point configurations and polytopes

Yakovlev,

Pichugina,

Koliechkina

2023

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The monograph is dedicated to exploring combinatorial point configurations derived from mapping a set of combinatorial configurations into Euclidean space. Various methods for this mapping, along with the typology and properties of the resultant configurations, are presented. In addition, the study revolves around combinatorial polytopes defined as convex hulls of combinatorial point configurations. The primary focus lies in examining multipermutation and partial multipermutation point configurations alongside their associated combinatorial polytopes known as multipermutohedra and partial multipermutohedra. Our theoretical contributions are substantiated through the proof of theorems and supporting auxiliary statements. Examples and illustrations are included to enhance the comprehension of the material.

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