41 citations · 136 across the 62 of their papers we have counts for
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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…
Fast Evaluation, Weights and Nonlinearity of Rotation-Symmetric Functions
Thomas W. Cusick, Pantelimon Stanica
We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu. We give exact results for the nonlinearity and weight of 2-degree Ro…
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…
p^q-Catalan Numbers and Squarefree Binomial Coefficients
Pantelimon Stanica
In this paper we consider the generalized Catalan numbers F(s,n)= 1/((s-1)n+1) binom{sn}{n}. We find all such that for prime, p^q divides F(p^q,n), q>=1. As a byproduct we…