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...

We give complexity analysis of the class of short generating functions (GF). Assuming #P 6⊆FP/poly, we show that this class is not closed under taking many intersections, unions or projections of GFs, in the sense that these operations can increase the bit length of coefficients of GFs by a super-polynomial factor. We also prove that truncated theta functions are hard in this class.

The randomized, deterministic and parallel algorithms for generating minimal perfect hash functions (MPHF) are proposed. Given a set of keys, W, which are character strings over some alphabet, the algorithms using a three-step approach (mapping, ordering, searching) nd the MPHF of the form h(w) = (h0(w) + g(h1(w)) + g(h2(w)))mod m, w 2 W, where h0, h1, h2 are auxiliary pseudorandom functions, m...

This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic expansion for the Taylor coefficients ofthe function. This approach is based on contour integration using Cauchy’s formula and Hankel-like contours. It constitutes an alternative to either Darboux’s method ...

In order to study precisely the growth of timed languages, we associate to such a language a generating function. These functions (tightly related to volume and entropy of timed languages) satisfy compositionality properties and, for deterministic timed regular languages, can be characterized by integral equations. We provide procedures for closed-form computation of generating functions for so...

This note settles an open problem about cut-generating functions, a concept that has its origin in the work of Gomory and Johnson from the 1970’s and has received renewed attention in recent years.

This paper introduces two related methods of generating a new cryptographic primitive termed digest which has similarities to -balanced and almost universal hash functions. Digest functions, however, typically have a very short output, e.g. 16-64 bits, and hence they are not required to resist collision and inversion attacks. They also have the potential to be very fast to compute relative to l...

We are going to discuss enumeration problems, and how to solve them using a powerful tool: generating functions. What is an enumeration problem? That’s trying to determine the number of objects of size n satisfying a certain definition. For instance, what is the number of permutations of {1, 2, . . . , n}? (answer: n!), or what is the number of binary sequences of length n? (answer: 2n). Ok, no...

We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating functions are the solutions of Hamilton-Jacobi equations. We obtain a purely categorical formulation of...

We show that the use of operational methods and of multi-index Bessel functions allow the derivation of generating functions, involving the product of an arbitrary number of Laguerre polynomials. ∗2000 Mathematics Subject Classification. 33C45, 44A45. †E-mail:[email protected] ‡E-mail:[email protected] §E-mail:[email protected] ¶E-mail:[email protected] 270 G. Dattol...