ON SEQUENCES OF ELEMENTARY TRANSFORMATIONS IN THE INTEGER PARTITIONS LATTICE
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
ON SEQUENCES OF ELEMENTARY TRANSFORMATIONS IN THE INTEGER PARTITIONS LATTICE
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| Автор |
Baransky, V. A.
Senchonok, T. A. |
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| Тематика |
ELEMENTARY TRANSFORMATION
FERRERS DIAGRAM INTEGER PARTITION INTEGER PARTITIONS LATTICE |
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| Описание |
An integer partition, or simply, a partition is a nonincreasing sequence λ = (λ1, λ2,…) of nonnegative integers that contains only a finite number of nonzero components. The length ℓ(λ) of a partition λ is the number of its nonzero components. For convenience, a partition λ will often be written in the form λ = (λ1,…,λt), where t ≥ ℓ(λ); i.e., we will omit the zeros, starting from some zero component, not forgetting that the sequence is infinite. Let there be natural numbers i, j ∈ {1,…,ℓ(λ) + 1} such that (1) λi − 1 ≥ λi+1; (2) λj−1 ≥ λj + 1; (3) λi = λj + δ, where δ ≥ 2. We will say that the partition η = (λ1,…, λi − 1, …, λj + 1, …, λn) is obtained from a partition λ = (λ1,…, λi,…, λj,…, λn) by an elementary transformation of the first type. Let λi − 1 ≥ λi+1, where i ≤ ℓ(λ). A transformation that replaces λ by η = (λ1,…,λi−1, λi − 1, λi+1, …) will be called an elementary transformation of the second type. The authors showed earlier that a partition µ dominates a partition λ if and only if λ can be obtained from µ by a finite number (possibly a zero one) of elementary transformations of the pointed types. Let λ and µ be two arbitrary partitions such that µ dominates λ. This work aims to study the shortest sequences of elementary transformations from µ to λ. As a result, we have built an algorithm that finds all the shortest sequences of this type. © 2023, Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
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| Дата |
2024-04-05T16:38:45Z
2024-04-05T16:38:45Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Baransky, V & Senchonok, T 2023, 'ON SEQUENCES OF ELEMENTARY TRANSFORMATIONS IN THE INTEGER PARTITIONS LATTICE', Ural Mathematical Journal, Том. 9, № 2, стр. 36-45. https://doi.org/10.15826/umj.2023.2.003
Baransky, V., & Senchonok, T. (2023). ON SEQUENCES OF ELEMENTARY TRANSFORMATIONS IN THE INTEGER PARTITIONS LATTICE. Ural Mathematical Journal, 9(2), 36-45. https://doi.org/10.15826/umj.2023.2.003 2414-3952 Final All Open Access, Gold https://www.scopus.com/inward/record.uri?eid=2-s2.0-85180819375&doi=10.15826%2fumj.2023.2.003&partnerID=40&md5=af909d6c931751154c083c9909aec4a9 https://umjuran.ru/index.php/umj/article/download/670/pdf http://elar.urfu.ru/handle/10995/131088 59690644 10.15826/umj.2023.2.003 85180819375 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Krasovskii Institute of Mathematics and Mechanics
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| Источник |
Ural Mathematical Journal
Ural Mathematical Journal |
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