Vol. 70, No. 1, 1977

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Enumeration of doubly up-down permutations

L. Carlitz

Vol. 70 (1977), No. 1, 105–116
Abstract

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

∑∞      -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 up-down (down-up) permutations in which the peaks themselves are in an up-down configuration.

In a previous paper the writer obtained generating functions for the number of up-down (and down-up) permutations counting the rises among the “peaks”.

Mathematical Subject Classification 2000
Primary: 05A15
Milestones
Received: 6 July 1976
Published: 1 May 1977
Authors
L. Carlitz