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We give an improved algorithm for counting the number of 1324-avoiding permu-tations, resulting in 5 further terms of the generating function. We analyse the known coefficients and find compelling evidence that unlike other classical length-4 pattern-avoiding permutations, the generating function in this case does not have an algebraic singularity. Rather, the number of 1324-avoiding permutations of length n behaves as B · µn · µnσ1 · ng. We estimate µ = 11.60 ± 0.01, σ = 1/2, µ1 = 0.0398 ± 0.0010, g = −1.1 ± 0.2 and B = 9.5 ± 1.0.
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permu...
AbstractLet σ∈Sk and τ∈Sn be permutations. We say τ contains σ if there exist 1⩽x1<x2<…<xk⩽n such th...
This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects n...
We show that the counting sequence for permutations avoiding both of the (clas-sical) patterns 1243 ...
We show that the counting sequence for permutations avoiding both of the(classical) patterns 1243 an...
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 consider permutations that avoid the pattern 1324. We give exact formulas for thenumber of reduci...
We establish a lower bound of 10.24 for the growth rate of the permutations avoiding 1324, and an up...
We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an u...
AbstractProving and disproving some earlier conjectures, we give a characterization of the numbers o...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permu...
AbstractWe study generating functions for the number of permutations on n letters avoiding 132 and a...
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...
AbstractLet σ∈Sk and τ∈Sn be permutations. We say τ contains σ if there exist 1⩽x1<x2<…<xk⩽n such th...
This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects n...
We show that the counting sequence for permutations avoiding both of the (clas-sical) patterns 1243 ...
We show that the counting sequence for permutations avoiding both of the(classical) patterns 1243 an...
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 consider permutations that avoid the pattern 1324. We give exact formulas for thenumber of reduci...
We establish a lower bound of 10.24 for the growth rate of the permutations avoiding 1324, and an up...
We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an u...
AbstractProving and disproving some earlier conjectures, we give a characterization of the numbers o...
Of the three Wilf classes of permutations avoiding a single pattern of length 4, the exact enumerati...
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permu...
AbstractWe study generating functions for the number of permutations on n letters avoiding 132 and a...
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...
AbstractLet σ∈Sk and τ∈Sn be permutations. We say τ contains σ if there exist 1⩽x1<x2<…<xk⩽n such th...
This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects n...
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