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The Number of Permutations with Exactlyr132-Subsequences IsP-Recursive in the Size!

✍ Scribed by Miklós Bóna

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 152 KB
Volume: 18
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1997.0528

No coin nor oath required. For personal study only.

✦ Synopsis

Proving a first nontrivial instance of a conjecture of Noonan and Zeilberger we Ž . show that the number S n of permutations of length n containing exactly r r subsequences of type 132 is a P-recursive function of n. We show that this remains true even if we impose some restrictions on the permutations. We also show the Ž . Ž . stronger statement that the ordinary generating function G x of S n is alger r ' braic, in fact, it is rational in the variables x and 1 y 4 x . We use this information Ž . to show that the degree of the polynomial recursion satisfied by S n is r. ᮊ 1997 r

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