A note on X-rays of permutations and a problem of Brualdi and Fritscher

TL;DR

This paper establishes a bijection between extremal Skolem sets and binary Hankel X-rays of permutation matrices, addressing a conjecture related to X-rays of permutations and Skolem sequences.

Contribution

It provides the first known bijection connecting extremal Skolem sets with binary Hankel X-rays of permutation matrices, advancing understanding of the conjecture.

Findings

Established a bijection between extremal Skolem sets and binary Hankel X-rays.

Provided new observations related to the conjecture on X-rays of permutations.

Addressed a problem posed by Brualdi and Fritscher in 2014.

Abstract

The subject of this note is a challenging conjecture about X-rays of permutations which is a special case of a conjecture regarding Skolem sequences. In relation to this, Brualdi and Fritscher [Linear Algebra and its Applications, 2014] posed the following problem: Determine a bijection between extremal Skolem sets and binary Hankel X-rays of permutation matrices. We give such a bijection, along with some related observations.