We give an improved algorithm for counting the number of 1324-avoiding permutations, resulting in 5 further terms of the generating function. We analyse the known coefficients and find compelling evidence that unlike other classical length-4 patternavoiding permutations, the generating function in this case does not have an algebraic singularity. Rather, the number of 1324-avoiding permutations...

The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...

The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...

We consider permutations which are 1324 and 2143 avoiding, where 2143 avoiding means that it is 2143 avoiding with the additional Bruhat restriction {2 ↔ 3}. In particular, for every permutation π we will construct a linear map Lπ and a labeled graph Gπ and will show that the following three conditions are equivalent: π is 1324 and 2143 avoiding; Lπ is onto; Gπ is a forest. We will also give so...

The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...

The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...

The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...

Classes of permutations are sets of permutations that are closed downwards under taking subpermutations. They are usually presented as sets C that avoid a given set B of permutations (i.e. the permutations of C have no subpermutation in the set B). We express this by the notation C = Av(B). Much of the inspiration for elucidating the structure of pattern classes has been driven by the enumerati...

The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lowe...