Vexillary Elements in the Hyperoctahedral Group
Journal of Algebraic Combinatorics: An International Journal
Discrete Mathematics - Kleitman and combinatorics: a celebration
Pattern frequency sequences and internal zeros
Advances in Applied Mathematics - Special issue: Memory of Rodica Simon
Small configurations in simple permutations
European Journal of Combinatorics
A Representation Theorem for Holonomic Sequences Based on Counting Lattice Paths
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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Proving a first nontrivial instance of a conjecture of Noonan and Zeilberger we show that the numberS"r(n) of permutations of lengthncontaining exactlyrsubsequences of type 132 is aP-recursive function ofn. We show that this remains true even if we impose some restrictions on the permutations. We also show the stronger statement that the ordinary generating functionG"r(x) ofS"r(n) is algebraic, in fact, it is rational in the variablesxand1-4x. We use this information to show that the degree of the polynomial recursion satisfied byS"r(n) isr.