Add to ORKGWe establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. These results depend on a new exact structural characterisation of 1324-avoiders as a subclass of an infinite staircase grid class, together with precise asymptotics of a small domino subclass whose enumeration we relate to West-two-stack-sortable permutations and planar maps. The bounds are established by carefully combining copies of the dominoes in particular ways consistent with the structural characterisation. The lower bound depends on concentration results concerning the substructure of a typical domino, the determination of exactly when dominoes can be combined in...
We determine the structure of permutations avoiding the patterns 4213 and2143. Each such permutation...
We establish a phase transition for permutation classes (downsets of permutations under the permutat...
Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as simila...
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permu...
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permu...
We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an u...
We establish a lower bound of 10.24 for the growth rate of the permutations avoiding 1324, and an up...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
We give an improved algorithm for counting the number of 1324-avoiding permu-tations, resulting in 5...
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combin...
This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects n...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutatio...
Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as simila...
We determine the structure of permutations avoiding the patterns 4213 and2143. Each such permutation...
We establish a phase transition for permutation classes (downsets of permutations under the permutat...
Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as simila...
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permu...
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permu...
We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an u...
We establish a lower bound of 10.24 for the growth rate of the permutations avoiding 1324, and an up...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
We give an improved algorithm for counting the number of 1324-avoiding permu-tations, resulting in 5...
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combin...
This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects n...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutatio...
Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as simila...
We determine the structure of permutations avoiding the patterns 4213 and2143. Each such permutation...
We establish a phase transition for permutation classes (downsets of permutations under the permutat...
Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as simila...