On the Basis Polynomials in the Theory of Permutations with Prescribed Up-Down Structure

Details On the Basis Polynomials in the Theory of Permutations with Prescribed Up-Down Structure On the Basis Polynomials in the Theory of Permutations with Prescribed Up-Down Structure

2007-12-30

arxiv.org/abs/0801.0072v2

Mathematics

Combinatorics

Revised argument in Section 13; results unchanged

Scientific paper

Let $\pi=(\pi_1,\pi_2,\hdots,\pi_n)$ be permutation of the elements
$1,2,\hdots,n. $ Positive integer $k\leq2^{n-1}$ we call index of $\pi,$ if in
its binary notation as $n$-digital binary number, the 1's correspond to the
ascent points. We study behavior and properties of numbers of permutations of
$n$ elements having index $k.$

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