In combinatorial mathematics, Catalan's triangle is a number triangle whose entries give the number of strings consisting of n X's and k Y's such that no initial segment of the string has more Y's than X's. It is a generalization of the Catalan numbers, and is named after Eugène Charles Catalan. Bailey shows that satisfy the following properties: 1.
* . 2.
* . 3.
* 4.
* . Shapiro introduces another triangle which he calls the Catalan triangle that is distinct from the triangle being discussed here.
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| - Catalan's triangle (en)
- Triangle de Catalan (fr)
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| - In combinatorial mathematics, Catalan's triangle is a number triangle whose entries give the number of strings consisting of n X's and k Y's such that no initial segment of the string has more Y's than X's. It is a generalization of the Catalan numbers, and is named after Eugène Charles Catalan. Bailey shows that satisfy the following properties: 1.
* . 2.
* . 3.
* 4.
* . Shapiro introduces another triangle which he calls the Catalan triangle that is distinct from the triangle being discussed here. (en)
- En mathématiques et plus précisément en combinatoire, le triangle de Catalan est un tableau triangulaire de nombres dont les termes, notés , donnent le nombre de mots constitués de n lettres X et p lettres Y, tels que tout segment initial possède plus ou autant de lettres X que de lettres Y. Lorsque , un tel mot est appelé un mot de Dyck, dont le nombre est le nombre de Catalan d'indice n, d'où le fait que ce triangle porte le nom d' Eugène Charles Catalan. Ce triangle est aussi en lien avec le problème du scrutin. (fr)
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| - In combinatorial mathematics, Catalan's triangle is a number triangle whose entries give the number of strings consisting of n X's and k Y's such that no initial segment of the string has more Y's than X's. It is a generalization of the Catalan numbers, and is named after Eugène Charles Catalan. Bailey shows that satisfy the following properties: 1.
* . 2.
* . 3.
* 4.
* . Formula 3 shows that the entry in the triangle is obtained recursively by adding numbers to the left and above in the triangle. The earliest appearance of the Catalan triangle along with the recursion formula is in page 214 of the treatise on Calculus published in 1800 by Louis François Antoine Arbogast. Shapiro introduces another triangle which he calls the Catalan triangle that is distinct from the triangle being discussed here. (en)
- En mathématiques et plus précisément en combinatoire, le triangle de Catalan est un tableau triangulaire de nombres dont les termes, notés , donnent le nombre de mots constitués de n lettres X et p lettres Y, tels que tout segment initial possède plus ou autant de lettres X que de lettres Y. Lorsque , un tel mot est appelé un mot de Dyck, dont le nombre est le nombre de Catalan d'indice n, d'où le fait que ce triangle porte le nom d' Eugène Charles Catalan. Ce triangle est aussi en lien avec le problème du scrutin. La première apparition des termes du triangle de Catalan définis par récurrence se trouve à la page 214 du traité publié en 1800 par Louis François Antoine Arbogast . Shapiro a appelé "triangle de Catalan" un autre triangle, distinct de celui-ci. (fr)
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