ON INVERSIONS AND CYCLES IN PERMUTATIONS

Abstract

Permutations consisting of a single cycle are considered. EDELMAN (1987) proved that such permutations contain at least n - 1 inversions. Moreover, he determined the number of such permutations having exactly n - 1 inversions: 2ⁿ-2. The present paper gives a new proof of the above statements and determines the number of such permutations having exactly n + 1 inversions.