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

Abstract

Let $π=(π_1,π_2,\hdots,π_n)$ be permutation of the elements $1,2,\hdots,n. $ Positive integer $k\le 2^{n-1}$ 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 $k.$

arXiv commentRevised argument in Section 13; results unchanged

Cited by in corpus (2)

• Equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x)$ for Thue-Morse sequence
• On Connection between the Numbers of Permutations and Full Cycles with Some Restrictions on Positions and Up-Down Structure