Euclidean Combinatorial Configurations: Continuous Representations and Convex Extensions

Pichugina, Oksana; Yakovlev, Sergiy

doi:10.1007/978-3-030-26474-1_5

Cited by 12 publications

(9 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this regard, we will use the concept of Euclidean combinatorial sets introduced by Yu. Stoyan in the preprints [74,75] and further studied in [53,59,60,[76][77][78][79][80][81]. In accordance with Yu.…”

Section: Introductionmentioning

confidence: 92%

Combinatorial point configurations and polytopes

Yakovlev,

Pichugina,

Koliechkina

2023

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 92%

Combinatorial point configurations and polytopes

Yakovlev,

Pichugina,

Koliechkina

2023

View full text Add to dashboard Cite

show abstract

“…Thus, if dimension of varieties ( 25) is n − 1, and f j (x), j ∈ J m \J m ′ are convex, C-set E is formed as an intersection of hypersurfaces (25) with convex bodies (26).…”

Section: Continuous Functional Representations Of C-setsmentioning

confidence: 99%

“…The presented results form the basis for the development of Euclidean combinatorial optimization methods [18,23,25,26,38,39,42,48,49,51,[53][54][55][56][57].Theoretically, it is of interest to develop new approaches to the construction of convex extensions of functions defined on the corresponding C b -sets. At that, it is natural to single out various special classes of C-sets, such as sets of e-configurations of permutation matrices, even, cyclic, or signed permutations, and so on.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

See 1 more Smart Citation

Continuous Extensions On Euclidean Combinatorial Configurations

Pichugina¹,

Yakovlev²

2022

BASM

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce a concept of the Euclidean combinatorial configuration as a mapping of a set of certain objects into a point of Euclidean space. We classify Euclidean combinatorial configurations sets based on their structure and constraints. The proposed typology forms the basis for studying continuous functional representations of combinatorial configurations. Special classes of functional extensions are introduced, their properties are described, and corresponding examples are given.

show abstract

“…Foodstuffs contain components such as carbohydrates, proteins, fats, vitamins, and other food components in known proportions. Knowing the minimum and maximum quantities of each food component that a person needs, as well as the supply and cost of that diet, we can develop plans to meet nutritional needs at the lowest cost and how to model diet menu problem (Pichugina, 2020). The problem of diet menus has been widely discussed in previous studies, especially when implementing linear programming.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model of Diet Menu Problem Based on Boolean Linear Programming Approach

Harahap

Nasution

Sawaluddin

2023

SinkrOn

View full text Add to dashboard Cite

This study aims to model the diet menu problem based on a Boolean Linear Programming approach. A balanced diet is the key to a healthy lifestyle. A balanced diet is a diet that combines foodstuffs in the right amount of food components in one menu (dishes using certain recipes). When you have an unbalanced diet, your body will not get the right amount of nutrients. This is what causes the importance of managing the diet menu. Because of that, a diet menu problem model was formed based on the Boolean Linear Programming approach to cover a varied range of daily diet menu management and meet daily nutritional needs while minimizing costs. The stages of establishing the diet menu problem model are carried out by determining the notations, parameters, variables, objective functions, and some constraints related to the diet menu.

show abstract

Euclidean Combinatorial Configurations: Continuous Representations and Convex Extensions

Cited by 12 publications

References 28 publications

Combinatorial point configurations and polytopes

Combinatorial point configurations and polytopes

Continuous Extensions On Euclidean Combinatorial Configurations

A Mathematical Model of Diet Menu Problem Based on Boolean Linear Programming Approach

Contact Info

Product

Resources

About