Vol. 45, No. 1, 1973

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Enumeration of up-down permutations by number of rises

L. Carlitz

Vol. 45 (1973), No. 1, 49–58
Abstract

It is well known that A(n), the number of up-down permutations of {1,2,,n} satisfies

∑𝜖      -z2n-
A(2n)(2n)! = secz,
n=0

∑∞           z2n+1
A(2n+ 1)(2n+-1)! = tanz.
n=0

In the present paper generating functions are obtained for the number of up-down permutations counting the number of rises among the “peaks”.

Mathematical Subject Classification 2000
Primary: 05A15
Milestones
Received: 17 November 1971
Published: 1 March 1973
Authors
L. Carlitz