We study the scaling behavior of the fluctuations, as extracted through wavelet coefficients based on discrete wavelets. The analysis is carried out on a variety of physical data sets, as well as Gaussian white noise and binomial multi-fractal model time series and the results are compared with continuous wavelet based average wavelet coefficient method. It is found that high-pass coefficients ...

In this article we offer group-theoretic, field-theoretic, and topological interpretations of the Gaussian binomial coefficients their sum. For a finite p-group G rank n, show that coefficient (nk)p is number subgroups are minimally expressible as an intersection n – k maximal G, sum precisely either or G. We provide field-theoretic interpretation these quantities through lens Galois theory inv...

Let (Cn)n≥0 be the Lucas sequence Cn+2 = aCn+1 +bCn for all n ≥ 0, where C0 = 0 and C1 = 1. For 1 ≤ k ≤ m− 1 let [ m k ] C = CmCm−1 · · ·Cm−k+1 C1 · · ·Ck be the corresponding C-nomial coefficient. When Cn = Fn is the Fibonacci sequence (the numbers [ m k ] F are called Fibonomials), or Cn = (qn − 1)/(q − 1), where q > 1 is an integer (the numbers [ m k ] q are called q-binomial, or Gaussian co...

We study some old and new problems involving divisors of the middle binomial coefficient (2n n ) .

A class of new type graded infinite posets with minimal element is introduced. These so called cobweb posets proposed recently by the present author constitute a wide range of new noncommutative and nonassociative prefab combinatorial schemes‘ examples with characteristic graded sub-posets as primes. These schemes are defined here via relaxing commutativity and associativity requirements impose...

In recent months I have come across many instances in which someone has found what they believe is a new result, in which they evaluate in closed form a sum involving binomial coefficients or factorials. In each case they have managed to do that either by using the recent powerful method of Wilf and Zeilberger (the W–Z method) [6], or by comparing coefficients in some ad hoc algebraic identity....