Some New Self-avoiding Walk and Polygon Models

• Autorzy: Beaton N. R. , Flajolet P. , Garoni T. M. , Guttmann A. J.
• Języki publikacji: EN

Abstrakty

EN

We study the behaviour of prudent, perimeter and quasi-prudent self-avoiding walks and polygons in both two and three dimensions, as well as some solvable subsets. Our analysis combines exact solutions of some simpler cases, careful asymptotic analysis of functional equations which can be obtained in more complicated cases and extensive numerical studies based on exact series expansions for less tractable cases, augmented by long Monte Carlo runs in some cases.

Słowa kluczowe

EN

prudent walks; prudent polygons; perimeter walks; quasi-prudent walks

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 117, nr 1-4
• Strony: 19--33
• Opis fizyczny: Bibliogr. 16 poz., tab., wykr.

Twórcy

autor

Beaton N. R.

autor

Flajolet P.

autor

Garoni T. M.

autor

Guttmann A. J.

• Department of Mathematics and Statistics The University of Melbourne VIC 3010 Australia,

Bibliografia

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• [2] Beaton, N. R., Flajolet, P. and Guttmann, A, J,: The enumeration of prudent polygons by area and its unusual asymptotics, J. Combin. Theory Ser. A, 118, 2011, 2261-2290.
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• [8] Flajolet, P. and Sedgewick, R.: Analytic Combinatorics, Cambridge University Press, 2009.
• [9] Garoni, T. M., Guttmann, A. J., Jensen, I. and Dethridge, J. C.: Prudent walks and polygons, J. Phys. A: Math. Theor., 42, 2009, 095205-095220.
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