Nikola Ruskuc

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It is known that the \pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally de ned subsets of permutations are partially well-ordered, in which case they have a strong nite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains(More)
Simple permutations are the building blocks of permutation classes. As such, classes with only finitely many simple permutations, e.g., the class of 132-avoiding permutations, have nice properties. To name three: these classes have algebraic generating functions (as established by Albert and Atkinson [1]; see Brignall, Huczynska, and Vatter [9] for(More)
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(More)
In this paper we give a description of all subsemigroups of the bicyclic monoid B. We show that there are essentially five different types of subsemigroups. One of them is the degenerate case, and the remaining four split in two groups of two, linked by the obvious anti-isomorphism of B. Each subsemigroup is characterized by a certain collection of(More)
This paper describes algorithms for computing the structure of finite transformation semigroups. The algorithms depend crucially on a new data structure for an R-class in terms of a group and an action. They provide for local computations, concerning a single R-class, without computing the whole semigroup, as well as for computing the global structure of(More)