Block design (original) (raw)
組合せ数学において、ブロックデザイン (block design) とは、実験計画法、ソフトウェアテスト、符号理論、暗号理論、有限幾何、代数幾何学などに広範な応用を持つハイパーグラフの一種である。ブロックデザインであることが文脈から明らかな場合、しばしば単に「デザイン」と呼ばれる。「デザイン」は「計画」と表記されることもある。
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| dbo:abstract | In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that frequency of the elements satisfies certain conditions making the collection of blocks exhibit symmetry (balance). They have applications in many areas, including experimental design, finite geometry, physical chemistry, software testing, cryptography, and algebraic geometry. Without further specifications the term block design usually refers to a balanced incomplete block design (BIBD), specifically (and also synonymously) a 2-design, which has been the most intensely studied type historically due to its application in the design of experiments. Its generalization is known as a t-design. (en) Ein Blockplan (auch Block-Design oder kombinatorisches Design) ist eine endliche Inzidenzstruktur, die insbesondere in der endlichen Geometrie, der Kombinatorik sowie der statistischen Versuchsplanung von Bedeutung ist. Blockpläne sind eine gemeinsame Verallgemeinerung der endlichen affinen Ebenen und der endlichen projektiven Ebenen. Wichtige Methoden zur Charakterisierung von Blockplänen und zur Konstruktion neuer Blockpläne aus bekannten sind die Auflösung und die taktische Zerlegung eines Blockplanes. Die Auflösung verallgemeinert das Konzept des Parallelismus eines Blockplanes, wie es dieser Artikel beschreibt, und ist selbst ein Spezialfall der taktischen Zerlegung. (de) En mathématiques combinatoires, un plan en blocs est un ensemble, muni d'une famille de sous-ensembles (avec des répétitions possibles) dont les membres satisfont un ensemble de propriétés considérées dans une application particulière. Les applications proviennent de nombreux domaines, notamment les plans d'expériences, la géométrie finie, la chimie physique, les tests de logiciels, la cryptographie et la géométrie algébrique. De nombreuses variantes ont été examinées, mais les plus étudiées sont les plans en blocs incomplets équilibrés (abrégé en BIBD pour balanced incomplete block designs (ou parfois 2-plans) qui sont historiquement liés à des problèmes statistiques dans la plans d'expériences. Un plan en blocs dans laquelle tous les blocs ont la même taille est appelé uniforme. Les plans décrits dans cette pages sont tous uniformes. Les plans équilibrées par paires sont des exemples de plans en blocs qui ne sont pas nécessairement uniformes. (fr) 組合せ数学において、ブロックデザイン (block design) とは、実験計画法、ソフトウェアテスト、符号理論、暗号理論、有限幾何、代数幾何学などに広範な応用を持つハイパーグラフの一種である。ブロックデザインであることが文脈から明らかな場合、しばしば単に「デザイン」と呼ばれる。「デザイン」は「計画」と表記されることもある。 (ja) 조합론에서 블록 설계(block設計, 영어: block design 블록 디자인[*])는 같은 크기의 일련의 부분 집합들이 주어져 있는 유한 집합이다. 이 경우, 이러한 부분 집합을 블록(영어: block)이라고 하며, 블록 설계는 (예를 들어) “개의 원소들을 포함하는 블록의 수는 원소의 선택에 상관없이 개”와 같은 꼴의 조건을 만족시켜야 한다. (ko) In matematica combinatoria il Disegno a blocchi è un insieme con una famiglia di sottoinsiemi (a volte sono consentiti sottoinsiemi ripetuti) i cui membri sono scelti per soddisfare un insieme di proprietà utili per una particolare applicazione.Queste applicazioni provengono da aree quali: la progettazione sperimentale, la geometria finita, la chimica-fisica, il test di software, la crittografia, e la geometrica algebrica.Son state studiate diverse variazioni, ma quelle più studiate sono i BIBD (balanced incomplete block design o 2-design)che sono storicamente correlate a problemi statistici nella progettazione di esperimenti. Un disegno a blocchi in cui tutti i blocchi hanno la stessa grandezza viene chiamato uniforme. (it) Блок-схема — это множество вместе с семейством подмножеств (повторение подмножеств разрешено в некоторых случаях), члены которого удовлетворяют некоторым свойствам, которые считаются полезными для конкретного приложения. Эти приложения приходят из разных областей, включая планирование эксперимента, конечную геометрию, тестирование программного обеспечения, криптографию и алгебраическую геометрию. Рассматривалось много вариантов, но наиболее интенсивно изучались сбалансированные неполные блок-схемы (Balanced Incomplete Block Designs, BIBD, 2-схемы), которые исторически были связаны со статистическими задачами при планировании эксперимента. Блок-схема, в которой все блоки имеют один размер, называется однородной. Схемы, обсуждаемые в этой статье, все однородны. Попарно сбалансированные схемы (Pairwise balanced designs, PBD) являются примерами блок-схем, которые не обязательно однородны. (ru) |
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| dbp:title | Block Designs (en) |
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| rdfs:comment | 組合せ数学において、ブロックデザイン (block design) とは、実験計画法、ソフトウェアテスト、符号理論、暗号理論、有限幾何、代数幾何学などに広範な応用を持つハイパーグラフの一種である。ブロックデザインであることが文脈から明らかな場合、しばしば単に「デザイン」と呼ばれる。「デザイン」は「計画」と表記されることもある。 (ja) 조합론에서 블록 설계(block設計, 영어: block design 블록 디자인[*])는 같은 크기의 일련의 부분 집합들이 주어져 있는 유한 집합이다. 이 경우, 이러한 부분 집합을 블록(영어: block)이라고 하며, 블록 설계는 (예를 들어) “개의 원소들을 포함하는 블록의 수는 원소의 선택에 상관없이 개”와 같은 꼴의 조건을 만족시켜야 한다. (ko) Ein Blockplan (auch Block-Design oder kombinatorisches Design) ist eine endliche Inzidenzstruktur, die insbesondere in der endlichen Geometrie, der Kombinatorik sowie der statistischen Versuchsplanung von Bedeutung ist. Blockpläne sind eine gemeinsame Verallgemeinerung der endlichen affinen Ebenen und der endlichen projektiven Ebenen. (de) In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that frequency of the elements satisfies certain conditions making the collection of blocks exhibit symmetry (balance). They have applications in many areas, including experimental design, finite geometry, physical chemistry, software testing, cryptography, and algebraic geometry. (en) En mathématiques combinatoires, un plan en blocs est un ensemble, muni d'une famille de sous-ensembles (avec des répétitions possibles) dont les membres satisfont un ensemble de propriétés considérées dans une application particulière. Les applications proviennent de nombreux domaines, notamment les plans d'expériences, la géométrie finie, la chimie physique, les tests de logiciels, la cryptographie et la géométrie algébrique. De nombreuses variantes ont été examinées, mais les plus étudiées sont les plans en blocs incomplets équilibrés (abrégé en BIBD pour balanced incomplete block designs (ou parfois 2-plans) qui sont historiquement liés à des problèmes statistiques dans la plans d'expériences. (fr) In matematica combinatoria il Disegno a blocchi è un insieme con una famiglia di sottoinsiemi (a volte sono consentiti sottoinsiemi ripetuti) i cui membri sono scelti per soddisfare un insieme di proprietà utili per una particolare applicazione.Queste applicazioni provengono da aree quali: la progettazione sperimentale, la geometria finita, la chimica-fisica, il test di software, la crittografia, e la geometrica algebrica.Son state studiate diverse variazioni, ma quelle più studiate sono i BIBD (balanced incomplete block design o 2-design)che sono storicamente correlate a problemi statistici nella progettazione di esperimenti. (it) Блок-схема — это множество вместе с семейством подмножеств (повторение подмножеств разрешено в некоторых случаях), члены которого удовлетворяют некоторым свойствам, которые считаются полезными для конкретного приложения. Эти приложения приходят из разных областей, включая планирование эксперимента, конечную геометрию, тестирование программного обеспечения, криптографию и алгебраическую геометрию. Рассматривалось много вариантов, но наиболее интенсивно изучались сбалансированные неполные блок-схемы (Balanced Incomplete Block Designs, BIBD, 2-схемы), которые исторически были связаны со статистическими задачами при планировании эксперимента. (ru) |
| rdfs:label | Blockplan (de) Block design (en) Plan en blocs (fr) Disegno a blocchi (it) 블록 설계 (ko) ブロックデザイン (数学) (ja) Блок-дизайн (ru) Блок-схема (математика) (uk) |
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