Geodesic
Consecutive up-down patterns in up-down permutations
Jeffrey B. Remmel1
1Department of Mathematics University of California, San Diego
The electronic journal of combinatorics, Tome 21 (2014) no. 3
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In this paper, we study the distribution of the number of consecutive pattern matches of the five up-down permutations of length four, $1324$, $2314$, $2413$, $1432$, and $3412$, in the set of up-down permutations. We show that for any such $\tau$, the generating function for the distribution of the number of consecutive pattern matches of $\tau$ in the set of up-down permutations can be expressed in terms of what we call the generalized maximum packing polynomials of $\tau$. We then provide some systematic methods to compute the generalized maximum packing polynomials for such $\tau$.
DOI : 10.37236/3210
Classification : 05A05, 05A15, 05E05
Mots-clés : up-down permutations, consecutive patterns, generating functions

Jeffrey B. Remmel  1

1 Department of Mathematics University of California, San Diego 
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     title = {Consecutive up-down patterns in up-down permutations},
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Jeffrey B. Remmel. Consecutive up-down patterns in up-down permutations. The electronic journal of combinatorics, Tome 21 (2014) no. 3. doi: 10.37236/3210

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