The Enumeration of Maximally Clustered Permutations

The Enumeration of Maximally Clustered Permutations

The maximally clustered permutations are characterized by avoiding the classical permutation patterns {3421, 4312, 4321}. This class contains the freely braided permutations and the fully commutative permutations. In this work, we show that the generating functions for certain fully commutative pattern classes can be transformed to give generating functions for the corresponding freely braided ...

The Enumeration of Simple Permutations

The enumeration of simple permutations

A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary generating function for simple permutations and that for all permutations, that the coefficients of this series are not P -recursive, an asymptotic expansion for ...

Enumeration of Pin-Permutations

In this paper, we study the class of pin-permutations, that is to say of permutations having a pin representation. This class has been recently introduced in [16], where it is used to find properties (algebraicity of the generating function, decidability of membership) of classes of permutations, depending on the simple permutations this class contains. We give a recursive characterization of t...

Efficient Enumeration of Graceful Permutations

A graceful n-permutation is a graceful labeling of an n-vertex path Pn. In this paper we improve the asymptotic lower bound on the number of such permutations from Ω((5/3)n) to Ω(2.37n). This is a computer-assisted proof based on an effective algorithm that enumerates graceful n-permutations. Our algorithm is also presented in detail. 1. Graceful graphs and permutations Let G = (V,E) be an undi...