On the X-rays of permutations

Cecilia Bebeacua, Toufik Mansour, Alex Postnikov, Simone Severini

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)193-203
Number of pages11
JournalElectronic Notes in Discrete Mathematics
StatePublished - 1 Jul 2005


  • Permutations
  • X-rays
  • score sequences of tournaments
  • zero-sum arrays

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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