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Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2003

On Generalized Delannoy Paths

Jean-Michel Autebert
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Résumé

A Delannoy path is a minimal path with diagonal steps in ${\mathbb Z}^2$ between two arbitrary points. We extend this notion to the $n$ dimensions space ${\mathbb Z}^n$ and identify such paths with words on a special kind of alphabet: an S-alphabet. We show that the set of all the words corresponding to Delannoy paths going from one point to another is exactly one class in the congruence generated by a Thue system that we exhibit. This Thue system induces a partial order on this set that is isomorphic to the set of ordered partitions of a fixed multiset where the blocks are sets with a natural order relation. Our main result is that this poset is a lattice.
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Dates et versions

hal-00084713 , version 1 (12-07-2006)

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  • HAL Id : hal-00084713 , version 1

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Jean-Michel Autebert, Sylviane R. Schwer. On Generalized Delannoy Paths. SIAM Journal on Discrete Mathematics, 2003, 16, pp.208-223. ⟨hal-00084713⟩
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