4 papers · 1 filter
Spectral Properties of a Binomial Matrix
Pantelimon Stanica, Rhodes Peele
In this paper we study some further properties of the matrix with entries binom{i-1}{n-j}. We find the generating function for each row and column, and we find the eigenvalues and…
Nonlinearity, Local and Global Avalanche Characteristics of Balanced Boolean Functions
Pantelimon Stanica
First, we construct a class of functions with good local avalanche characteristics, but bad global avalanche characteristics. We also derive some bounds for the nonlinearity of suc…
Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences
Rhodes Peele, Pantelimon Stanica
If L, respectively R are matrices with entries binom{i-1,j-1}, respectively binom{i-1,n-j}, it is known that L^2 = I (mod 2), respectively R^3 = I (mod 2), where I is the identity…
Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences
Pantelimon Stanica
In this paper we find closed form for the generating function of powers of any non-degenerate second-order recurrence sequence, completing a study begun by Carlitz and Riordan in 1…