Strongly restricted permutations and tiling with fences

Tiling the Plane with Permutations

A permutomino is a polyomino uniquely defined by a pair of permutations. Recently permutominoes, and in particular convex permutominoes have been studied by several authors concerning their analytical and bijective enumeration, tomographical reconstruction, and the algebraic characterization of the associated permutations [2, 3]. On the other side, Beauquier and Nivat [5] introduced and gave a ...

Permutations with Restricted Position

6. Concluding Remarks. Preliminary analysis indicates that parallel computation, using modular arithmetic, is feasible for certain kinds of problems. The parallel computation envisioned here leads very swiftly to a solution encoded "in modular notation." By this is meant, a system of simultaneous congruences, whose solution (in a specified interval), written as a binary number, has as its initi...

Solving Tiling Using Optimal Permutations

Simple permutations and pattern restricted permutations

A simple permutation is one that does not map any non-trivial interval onto an interval. It is shown that, if the number of simple permutations in a pattern restricted class of permutations is finite, the class has an algebraic generating function and is defined by a finite set of restrictions. Some partial results on classes with an infinite number of simple permutations are given. Examples of...

Restricted permutations

Restricted permutations are those constrained by having to avoid subsequences ordered in various prescribed ways. They have functioned as a convenient descriptor for several sets of permutations which arise naturally in combinatorics and computer science. We study the partial order on permutations (and more general sequences) that underlies the idea of restriction and which gives rise to sets o...