On the X-rays of permutations

Details On the X-rays of permutations On the X-rays of permutations

2005-06-16

arxiv.org/abs/math/0506334v1

Electronic Notes in Discrete Mathematics, Vol. 20, 2005, pp. 193-203

Mathematics

Combinatorics

7 pages

Scientific paper

The X-ray of a permutation is defined as the sequence of antidiagonal sums in the associated permutation matrix. X-rays of permutation are interesting in the context of Discrete Tomography since many types of integral matrices can be written as linear combinations of permutation matrices. This paper is an invitation to the study of X-rays of permutations from a combinatorial point of view. We present connections between these objects and nondecreasing differences of permutations, zero-sum arrays, decomposable permutations, score sequences of tournaments, queens' problems and rooks' problems.

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