Deflatability of Permutation Classes
M. H. Albert, M. D. Atkinson, Cheyne Homberger, Jay Pantone
TL;DR
This paper investigates the concept of deflatability in permutation classes, providing criteria for non-deflatability, and illustrating examples of both deflatable and non-deflatable classes to enhance understanding and classification.
Contribution
It introduces new theorems for identifying non-deflatable permutation classes and offers examples of principal classes demonstrating deflatability properties.
Findings
Theorems guaranteeing non-deflatability are proved.
Examples of deflatable principal classes are provided.
Examples of non-deflatable principal classes are given.
Abstract
A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee non-deflatability are proved and examples of both deflatable and non-deflatable principal classes are given.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · semigroups and automata theory