Shortened universal cycles for permutations

Kitaev et al. (2019) described how to shorten universal words for permutations, to length n! + n - 1 - i(n - 1) for any i is an element of [(n - 2)!], by introducing incomparable elements. They conjectured that it is also possible to use incomparable elements to shorten universal cycles for permutations to length n! - i(n - 1) for any i is an element of [(n - 2)!]. In this note we prove their conjecture. The proof is constructive, and, on the way, we also show a new method for constructing universal cycles for permutations.(c) 2022 Elsevier B.V. All rights reserved.