Pattern Avoidance Classes and Subpermutations

  • M. D. Atkinson
  • M. M. Murphy
  • N. Ruškuc


Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers a structure theorem is given. The structure theorem shows that the class is almost closed under direct sums or has a rational generating function.

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