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 |
INTEGER PARTITION
FERRERS DIAGRAM INTEGER PARTITIONS LATTICE ELEMENTARY TRANSFORMATION |
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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.
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| Дата |
2024-02-14T05:20:45Z
2024-02-14T05:20:45Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Baransky V. A. ON SEQUENCES OF ELEMENTARY TRANSFORMATIONS IN THE INTEGER PARTITIONS LATTICE / V. A. Baransky, T. A. Senchonok. — Text : electronic // Ural Mathematical Journal. — 2023. — Volume 9. — № 2. — P. 36-45.
2414-3952 https://umjuran.ru/index.php/umj/article/view/670 http://elar.urfu.ru/handle/10995/129431 59690644 10.15826/umj.2023.2.003 |
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| Язык |
en
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| Связанные ресурсы |
Ural Mathematical Journal. 2023. Volume 9. № 2
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| Права |
Creative Commons Attribution License
https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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