 School of Mathematics and Statistics  Research Publications
School of Mathematics and Statistics  Research Publications
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ItemAsymptotics of 3StackSortable PermutationsDefant, C ; Price, AE ; Guttmann, AJ (ELECTRONIC JOURNAL OF COMBINATORICS, 20210618)We derive a simple functional equation with two catalytic variables characterising the generating function of 3stacksortable permutations. Using this functional equation, we extend the 174term series to 1000 terms. From this series, we conjecture that the generating function behaves as $$W(t) \sim C_0(1\mu_3 t)^\alpha \cdot \log^\beta(1\mu_3 t), $$ so that $$[t^n]W(t)=w_n \sim \frac{c_0\mu_3^n}{ n^{(\alpha+1)}\cdot \log^\lambda{n}} ,$$ where $\mu_3 = 9.69963634535(30),$ $\alpha = 2.0 \pm 0.25.$ If $\alpha = 2$ exactly, then $\lambda = \beta+1$, and we estimate $\beta \approx 2,$ but with a wide uncertainty of $\pm 1.$ If $\alpha$ is not an integer, then $\lambda=\beta$, but we cannot give a useful estimate of $\beta$. The growth constant estimate (just) contradicts a conjecture of the first author that $$9.702 < \mu_3 \le 9.704.$$ We also prove a new rigorous lower bound of $\mu_3\geq 9.4854$, allowing us to disprove a conjecture of Bóna. We then further extend the series using differentialapproximants to obtain approximate coefficients $O(t^{2000}),$ expected to be accurate to $20$ significant digits, and use the approximate coefficients to provide additional evidence supporting the results obtained from the exact coefficients.

ItemSelfavoiding walks in a rectangleGuttmann, AJ ; Kennedy, T (SPRINGER, 20140201)

ItemThe Critical Fugacity for Surface Adsorption of SelfAvoiding Walks on the Honeycomb Lattice isBeaton, NR ; BousquetMelou, M ; de Gier, J ; DuminilCopin, H ; Guttmann, AJ (SPRINGER, 20140301)

ItemCompressed selfavoiding walks, bridges and polygonsBeaton, NR ; Guttmann, AJ ; Jensen, I ; Lawler, GF (IOP PUBLISHING LTD, 20151113)

ItemFuchsian differential equation for the perimeter generating function of threechoice polygonsGUTTMANN, A ; JENSEN, I ( 2005)

ItemScaling function and universal amplitude combinations for selfavoiding polygonsRichard, C ; Guttmann, AJ ; Jensen, I (IOP PUBLISHING LTD, 20010914)

ItemThe perimeter generating function of punctured staircase polygonsGuttmann, AJ ; Jensen, I (IOP PUBLISHING LTD, 20060414)

ItemScaling prediction for selfavoiding polygons revisitedRichard, C ; Jensen, I ; Guttmann, AJ (IOP PUBLISHING LTD, 20040801)

ItemVicious walkers, friendly walkers, and young tableaux. III. Between two wallsKrattenthaler, C ; Guttmann, AJ ; Viennot, XG (SPRINGER, 20030301)

ItemCritical behavior of the twodimensional Ising susceptibilityOrrick, WP ; Nickel, BG ; Guttmann, AJ ; Perk, JHH (AMERICAN PHYSICAL SOC, 20010430)We report computations of the short and longdistance (scaling) contributions to the squarelattice Ising susceptibility. Both computations rely on summation of correlation functions, obtained using nonlinear partial difference equations. In terms of a temperature variable tau, linear in T/Tc1, the shortdistance terms have the form tau(p)(ln/tau/)q with p> or =q2. A high and lowtemperature series of N = 323 terms, generated using an algorithm of complexity O(N6), are analyzed to obtain the scaling part, which when divided by the leading /tau/(7/4) singularity contains only integer powers of tau. Contributions of distinct irrelevant variables are identified and quantified at leading orders /tau/(9/4) and /tau/(17/4).