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Combinatoria algebrica Algebraic combinatorics Combinatoria algebraica 代數組合學 Combinatoire algébrique Алгебрична комбінаторика Алгебраическая комбинаторика
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En mathématiques, la combinatoire algébrique est une discipline qui traite de l'étude des structures algébriques par des techniques algorithmiques et combinatoires, comme notamment illustré par les travaux de Marcel-Paul Schützenberger, Alain Lascoux, Dominique Foata, Richard Peter Stanley… Алгебрична комбінаторика — це галузь математики, що використовує методи загальної алгебри, особливо теорії груп і теорії представлень, у різних комбінаторних контекстах і, навпаки, застосовує комбінаторні техніки до задач в алгебрі. La combinatoria algebrica è un'area della matematica dai contorni in progressiva definizione che utilizza metodi dell'algebra astratta, facendo riferimento in particolare alle strutture della teoria dei gruppi e della teoria delle rappresentazioni, per affrontare numerosi problemi di natura combinatoria e per converso si serve di configurazioni combinatorie e di tecniche algoritmico-combinatorie per analizzare strutture e problemi dell'algebra astratta. Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. La combinatoria algebraica es un área de las matemáticas que emplea métodos del álgebra abstracta, notablemente la teoría de grupos y la teoría de representación, en varios contextos de la combinatoria y, a la inversa, aplica técnicas combinatorias a problemas de álgebra. 代數組合學是組合數學中與抽象代數相關的分支,它可以意指解決組合問題的抽象代數方法,或涉及代數問題的組合學方法。相關的數學課題包括了 * 擬陣 * 多胞體 * 有限幾何 * * 格 (數學) Алгебраическая комбинаторика — это область математики, использующая методы общей алгебры, в особенности теории групп и теории представлений, в различных комбинаторных контекстах и, наоборот, применяющая комбинаторные техники к задачам в алгебре.
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Алгебрична комбінаторика — це галузь математики, що використовує методи загальної алгебри, особливо теорії груп і теорії представлень, у різних комбінаторних контекстах і, навпаки, застосовує комбінаторні техніки до задач в алгебрі. La combinatoria algebrica è un'area della matematica dai contorni in progressiva definizione che utilizza metodi dell'algebra astratta, facendo riferimento in particolare alle strutture della teoria dei gruppi e della teoria delle rappresentazioni, per affrontare numerosi problemi di natura combinatoria e per converso si serve di configurazioni combinatorie e di tecniche algoritmico-combinatorie per analizzare strutture e problemi dell'algebra astratta. Lo sviluppo di quest'area è piuttosto recente e i suoi contorni sono in progressiva definizione. Molte delle sue tematiche hanno avuto sviluppi di rilievo a partire dal 1964, ma senza riuscire a far emergere un'area fino al 1980. In effetti, nella prefazione del suo testo Combinatorial Theory, pubblicato nel 1979 e molto influente negli anni 1980, Martin Aigner segnala il "crescente consenso sulla opportunità che la combinatoria si divida in tre parti (Enumerazione, teoria degli ordini e Configurazioni)", senza neppure menzionare il termine combinatoria algebrica. Negli anni 1980 la progressiva crescita degli studi concernenti la congiunzione di metodi combinatorici e algebrici hanno condotto alla introduzione nella versione del 1991 dello schema di classificazione MSC della categoria di secondo livello 05Exx intitolata Combinatoria algebrica. Nel corso dei primi e intermedi anni 1990 i tipici oggetti combinatorici di interesse per la combinatoria algebrica o presentavano marcate simmetrie , oppure possedevano una ricca struttura algebrica, che spesso aveva origine nella teoria delle rappresentazioni (funzioni simmetriche, tabelle di Young). I risultati acquisiti e consolidati negli anni successivi hanno fatto considerare la combinatoria algebrica come un'area della matematica sempre più estesa, nella quale le interazioni fra metodi combinatorici e algebrici sono particolarmente forti e significative. Gli argomenti combinatorici possono essere negli scopi specifici, e coinvolgere strutture come matroidi, , posets o geometrie finite. Sul versante algebrico, oltre alle teorie dei gruppi e delle rappresentazioni, sono cresciuti i ruoli della teoria dei reticoli e dell'algebra commutativa. Una delle sue sotto-aree di maggiore crescita è l'. Questi sviluppi hanno ricevuto riconoscimento dal consolidarsi della categoria 05Exx nelle versioni di MSC del 2000 e del 2010. In particolare la modifica più recente (v. [1]) vede sistematici ampliamenti della portata delle categorie di terzo livello. Il recente progressivo consolidamento della combinatoria algebrica è rispecchiato anche dalla pubblicazione di testi autorevoli sull'argomento, dalla rilevanza della rivista pubblicata dalla Springer-Verlag (periodico scientifico internazionale che si propone come forum per quest'area), e dalla organizzazione di alcune serie di convegni. En mathématiques, la combinatoire algébrique est une discipline qui traite de l'étude des structures algébriques par des techniques algorithmiques et combinatoires, comme notamment illustré par les travaux de Marcel-Paul Schützenberger, Alain Lascoux, Dominique Foata, Richard Peter Stanley… 代數組合學是組合數學中與抽象代數相關的分支,它可以意指解決組合問題的抽象代數方法,或涉及代數問題的組合學方法。相關的數學課題包括了 * 擬陣 * 多胞體 * 有限幾何 * * 格 (數學) Алгебраическая комбинаторика — это область математики, использующая методы общей алгебры, в особенности теории групп и теории представлений, в различных комбинаторных контекстах и, наоборот, применяющая комбинаторные техники к задачам в алгебре. Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra. La combinatoria algebraica es un área de las matemáticas que emplea métodos del álgebra abstracta, notablemente la teoría de grupos y la teoría de representación, en varios contextos de la combinatoria y, a la inversa, aplica técnicas combinatorias a problemas de álgebra.
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