Annals of Combinatorics

, Volume 14, Issue 3, pp 291–306 | Cite as

On the Probability that Certain Compositions Have the Same Number Of Parts

Article

Abstract

We compute the asymptotic probability that two randomly selected compositions of n into parts equal to a or b have the same number of parts. In addition, we provide bijections in the case of parts of sizes 1 and 2 with weighted lattice paths and central Whitney numbers of fence posets. Explicit algebraic generating functions and asymptotic probabilities are also computed in the case of pairs of compositions of n into parts at least d, for any fixed natural number d.

AMS Subject Classification

05A05 05A15 05A16 

Keywords

composition probability lattice paths fence poset asymptotics 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.School of MathematicsUniversity of theWitwatersrand, JohannesburgWITSSouth Africa

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