Lagrange inversion over finite fields

Classical Wavelet Transforms over Finite Fields

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...

Classical wavelet systems over finite fields

This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

Efficient Inversion of Rational Maps over Finite Fields

We study the problem of finding the inverse image of a point in the image of a rational map F : F q → F n q over a finite field Fq. Our interest mainly stems from the case where F encodes a permutation given by some public–key cryptographic scheme. Given an element y(0) ∈ F (F q ), we are able to compute the set of values x(0) ∈ F q for which F (x(0)) = y(0) holds with O(Tn4.38D2.38δ log q) bit...

The Lagrange Inversion Formula Onnon { Archimedean Fields . Non { Analytical Form Ofdifferential and Finite Difference Equations

Lagrange inversion

We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.