Haruspicy and anisotropic generating functions
نویسندگان
چکیده
منابع مشابه
Haruspicy and anisotropic generating functions
Guttmann and Enting [Phys. Rev. Lett. 76 (1996) 344–347] proposed the examination of anisotropic generating functions as a test of the solvability of models of bond animals. In this article we describe a technique for examining some properties of anisotropic generating functions. For a wide range of solved and unsolved families of bond animals, we show that the coefficients of yn is rational, t...
متن کاملHaruspicy 2: The anisotropic generating function of self-avoiding polygons is not D-finite
We prove that the anisotropic generating function of self-avoiding polygons is not a D-finite function—proving a conjecture of Guttmann [Discrete Math. 217 (2000) 167–189] and Guttman and Enting [Phys. Rev. Lett. 76 (1996) 344–347]. This result is also generalised to self-avoiding polygons on hypercubic lattices. Using the haruspicy techniques developed in an earlier paper [Rechnitzer, Adv. App...
متن کاملHaruspicy 3: The anisotropic generating function of directed bond-animals is not D-finite
While directed site-animals have been solved on several lattices, directed bond-animals remain unsolved on any nontrivial lattice. In this paper we demonstrate that the anisotropic generating function of directed bond-animals on the square lattice is fundamentally different from that of directed site-animals in that it is not differentiably finite. We also extend this result to directed bond-an...
متن کاملOn composition of generating functions
In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...
متن کاملTutte polynomials of wheels via generating functions
We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2003
ISSN: 0196-8858
DOI: 10.1016/s0196-8858(02)00534-1