On the Probability that Certain Compositions Have the Same Number Of Parts
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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 Classification05A05 05A15 05A16
Keywordscomposition probability lattice paths fence poset asymptotics
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