Geometric grid classes of permutations
By Michael Henry Albert, M. Atkinson, Mathilde Bouvel, Nik Ruvskuc, Vincent Vatter. 2011
89 citations recorded by the source corpus.
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods, we prove that such classes are specified by finite sets of forbidden permutations, are partially well ordered, and have rational generating functions. Furthermore, we show that these properties are inherited by the subclasses (under permutation involvement) of such classes, and establish the basic lattice theoretic properties of the collection of all such subclasses.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Genetics
View Paper: https://www.semanticscholar.org/paper/001c1c53c1862a6c44c97323ec9bbaa1eab3057c
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
In Genetics
Citations in the corpus
- Permutation classes (2014, methodology): “This latter work has since been refined by Bóna, Homberger, Pantone, and Vatter [55] to enumerate the involutions in the classes Av(1342) and Av(2341).”