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- En mathématiques, et notamment en combinatoire, le graphe de Young-Fibonacci et le treillis de Young-Fibonacci, appelés ainsi d'après Alfred Young et Leonardo Fibonacci, sont deux structures voisines sur des suites composées exclusivement de chiffres 1 et 2. On appelle rang d'une suite de chiffres la somme de ses chiffres ; par exemple, le rang de 11212 est 1 + 1 + 2 + 1 + 2 = 7. On démontre ci-dessous que le nombre de suites de rang donné est un nombre de Fibonacci. Le treillis de Young-Fibonacci est le treillis modulaire dont les éléments sont ces suites de chiffres et qui est compatible avec cette structure de rang. Le graphe de Young-Fibonacci est le graphe du diagramme de Hasse de ce treillis, et il a un sommet pour chacune de ces suites de chiffres. Les graphe et treillis de Young-Fibonacci ont été étudiés initialement dans deux articles de et . Ils sont appelés ainsi à cause de leur étroite parenté avec le treillis de Young, et à cause du lien avec les nombres de Fibonacci. (fr)
- In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. Any digit sequence of this type can be assigned a rank, the sum of its digits: for instance, the rank of 11212 is 1 + 1 + 2 + 1 + 2 = 7. As was already known in ancient India, the number of sequences with a given rank is a Fibonacci number. The Young–Fibonacci lattice is an infinite modular lattice having these digit sequences as its elements, compatible with this rank structure. The Young–Fibonacci graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph. The Young–Fibonacci graph and the Young–Fibonacci lattice were both initially studied in two papers by and . They are named after the closely related Young's lattice and after the Fibonacci number of their elements at any given rank. (en)
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- En mathématiques, et notamment en combinatoire, le graphe de Young-Fibonacci et le treillis de Young-Fibonacci, appelés ainsi d'après Alfred Young et Leonardo Fibonacci, sont deux structures voisines sur des suites composées exclusivement de chiffres 1 et 2. On appelle rang d'une suite de chiffres la somme de ses chiffres ; par exemple, le rang de 11212 est 1 + 1 + 2 + 1 + 2 = 7. (fr)
- In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. Any digit sequence of this type can be assigned a rank, the sum of its digits: for instance, the rank of 11212 is 1 + 1 + 2 + 1 + 2 = 7. As was already known in ancient India, the number of sequences with a given rank is a Fibonacci number. The Young–Fibonacci lattice is an infinite modular lattice having these digit sequences as its elements, compatible with this rank structure. The Young–Fibonacci graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph. (en)
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- Treillis de Young-Fibonacci (fr)
- Young–Fibonacci lattice (en)
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