On Connection between the Numbers of Permutations and Full Cycles with Some Restrictions on Positions and Up-Down Structure

Abstract

We discuss both simple and more subtle connections between the numbers of permutations and full cycles with some restrictions,in particular, between the numbers of permutations and full cycles with prescribed up-down structure.

Revised arguments in Sections 2,3, results unchanged

References in corpus (1)

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

Cited by in corpus (1)

• Equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x)$ for Thue-Morse sequence