3 citations · 4 across the 8 of their papers we have counts for
10 papers
Enumerating Pattern-Avoiding Involutions using Combinatorial Exploration
Christian Bean, Anthony J. Guttmann, Jay Pantone
The enumeration of pattern-avoiding permutations has been a popular area of study over the past several decades, but comparatively little attention has been given to the topic of p…
Restricted Permutations Enumerated by Inversions
Atli Fannar Franklín, Anders Claesson, Christian Bean +2
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposab…
Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding
Christian Bean, Émile Nadeau, Jay Pantone +1
We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational gener…
Combinatorial Exploration: An algorithmic framework for enumeration
Michael H. Albert, Christian Bean, Anders Claesson +3
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequ…
On the generating functions of pattern-avoiding Motzkin paths
Christian Bean, Antonio Bernini, Matteo Cervetti +1
Using a recursive approach, we show that the generating function for sets of Motzkin paths avoiding a single (not necessarily consecutive) pattern is rational over and the Cata…
Enumeration of Permutation Classes and Weighted Labelled Independent Sets
Christian Bean, Émile Nadeau, Henning Ulfarsson
In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cells filled with permutations. We consider many cases, where rest…
Algorithmic coincidence classification of mesh patterns
Christian Bean, Bjarki Gudmundsson, Tomas Ken Magnusson +1
We review and extend previous results on coincidence of mesh patterns. We introduce the notion of a force on a permutation pattern and apply it to the coincidence classification of…
Automatic discovery of structural rules of permutation classes
Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson
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 usuall…
Pattern avoiding permutations and independent sets in graphs
Christian Bean, Murray Tannock, Henning Ulfarsson
We introduce a new method for encoding permutations as weighted independent sets in a family of graphs we call cores. The encoding allows us to enumerate (1324, 2143)-, (1234, 1324…
Enumerations of Permutations Simultaneously Avoiding a Vincular and a Covincular Pattern of Length 3
Christian Bean, Anders Claesson, Henning Ulfarsson
Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we stu…