Related papers: Permutations avoiding bipartite partially ordered …
Partially ordered patterns (POPs) play an important role in the study of permutation patterns, providing a convenient framework for describing large families of classical patterns. The problem of enumerating permutations that avoid POPs has…
A permutation $\pi$ contains a pattern $\sigma$ if and only if there is a subsequence in $\pi$ with its letters are in the same relative order as those in $\sigma$. Partially ordered patterns (POPs) provide a convenient way to denote…
A partially ordered (generalized) pattern (POP) is a generalized pattern some of whose letters are incomparable, an extension of generalized permutation patterns introduced by Babson and Steingrimsson. POPs were introduced in the symmetric…
Partially ordered patterns (POPs) generalize the notion of classical patterns studied widely in the literature in the context of permutations, words, compositions and partitions. In an occurrence of a POP, the relative order of some of the…
Partially ordered patterns (POPs) generalize the notion of classical patterns studied in the literature in the context of permutations, words, compositions and partitions. In this paper, we give a number of general, and specific enumerative…
Despite the fact that the field of pattern avoiding permutations has been skyrocketing over the last two decades, there are very few exhaustive generating algorithms for such classes of permutations. In this paper we introduce the notions…
A partially ordered pattern (abbreviated POP) is a partially ordered set (poset) that generalizes the notion of a pattern when we are not concerned with the relative order of some of its letters. The notion of partially ordered patterns…
We prove that every proper subclass of the 321-avoiding permutations that is defined either by only finitely many additional restrictions or is well quasi-ordered has a rational generating function. To do so we show that any such class is…
Partially ordered patterns (POPs) generalize classical permutation patterns and have been extensively studied in the contexts of permutations, words, compositions, and partitions. Burstein, Han, Kitaev, and Zhang established the…
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…
Finding distributions of statistics in pattern-avoiding permutations has attracted significant attention in the literature. In particular, Chen, Kitaev, and Zhang derived functional equations for the joint distributions of any subset of…
We study generating functions for the number of involutions in $S_n$ avoiding (or containing once) 132, and avoiding (or containing once) an arbitrary permutation $\tau$ on $k$ letters. In several interesting cases the generating function…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
Partially ordered patterns (POPs) generalize the classical notion of permutation patterns within the framework of pattern avoidance. Building on recent work by Burstein, Han, Kitaev, and Zhang, which introduced the concept of…
The maximally clustered permutations are characterized by avoiding the classical permutation patterns 3421, 4312, and 4321. This class contains the freely-braided permutations and the fully-commutative permutations. In this work, we show…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…
We adapt the vertical and horizontal insertion encodings of Cayley permutations to enumerate restricted growth functions, which are in bijection with unordered set partitions. For both insertion encodings, we fully classify the classes for…
We consider the set of permutations that are sorted after two passes through a pop stack. We characterize these permutations in terms of forbidden patterns (classical and barred) and enumerate them according to the ascent statistic. Then we…
Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these are the two main tools in the recent classification of…