Journal article
On 1324-avoiding permutations
AR Conway, AJ Guttmann
Advances in Applied Mathematics | Published : 2015
Abstract
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 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 · μ1nσ · ng. We estimate μ = 11.60 ± 0.01, σ = 1/2, μ1 = 0.040 ± 0.0015, g = -1.1 ± 0.2 and B = 7 ± 1.3.
Grants
Awarded by Australian Research Council
Funding Acknowledgements
A.J.G. wishes to acknowledge helpful conversations with Einar Steingrimsson, who brought this problem to our attention, and the hospitality of Mathematisches Forschungsinstitut Oberwolfach and the Enumerative Combinatorics Workshop held there on March 2-8, 2014, where this work was initiated. We also thank Neal Madras for helpful discussions and some unpublished Monte Carlo data. We are grateful to Alan Sokal, who gave us access to his Dell computers with 1 TB memory, which were needed for these calculations, through his NSF grant PHY-0424082 NYU. A.J.G. wishes to thank the Australian Research Council for supporting this work through grant DP120100931.