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

Vladimir Shevelev

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

Combinatorics 2010-09-23 v2

Authors: Vladimir Shevelev

Abstract

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 $k.$

Keywords

permutations up-down structure basis polynomials ascent points binary notation combinatorial properties

Cite

@article{arxiv.0801.0072,
  title  = {On the Basis Polynomials in the Theory of Permutations with Prescribed Up-Down Structure},
  author = {Vladimir Shevelev},
  journal= {arXiv preprint arXiv:0801.0072},
  year   = {2010}
}

Comments

Revised argument in Section 13; results unchanged

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

Abstract

Keywords

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