Geodesic
The Martin boundary of the Young-Fibonacci lattice
Journal of Algebraic Combinatorics, Tome 11 (2000) no. 1, pp. 17-48.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we find the Martin boundary for the Young-Fibonacci lattice YF. Along with the lattice of Young diagrams, this is the most interesting example of a differential partially ordered set. The Martin boundary construction provides an explicit Poisson-type integral representation of non-negative harmonic functions on YF. The latter are in a canonical correspondence with a set of traces on the locally semisimple Okada algebra. The set is known to contain all the indecomposable traces. Presumably, all of the traces in the set are indecomposable, though we have no proof of this conjecture. Using an explicit product formula for Okada characters, we derive precise regularity conditions under which a sequence of characters of finite-dimensional Okada algebras converges.
Keywords: differential poset, harmonic function, martin boundary, okada algebra, non-commutative symmetric function 
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     title = {The {Martin} boundary of the {Young-Fibonacci} lattice},
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Goodman, Frederick M.; Kerov, Sergei V. The Martin boundary of the Young-Fibonacci lattice. Journal of Algebraic Combinatorics, Tome 11 (2000) no. 1, pp. 17-48. http://geodesic.mathdoc.fr/item/JAC_2000__11_1_a3/