Elsevier

Discrete Mathematics

Volume 4, Issue 3, March 1973, Pages 273-286
Discrete Mathematics

Enumeration of up-down sequences*

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Abstract

Generalizing the notion of up-down permutations, the author considers sequences σ = (a1, a2, , αN) of length N = s2 + s2 ++ sn, where αi ∈ {1, 2,n } and the element j occurs exactly sj times. The repeated elements of a are labeled i, i′, i″, and it is assumed that they occur in a m natural order. Generating functions for the number of up-down sequences are constructed. Making use of the generating functions, explicit formulas for the number of up-down sequences are obtained.

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Supported in part by NSF grant No. GP 17031