Consider a prime number p. Let vp be the p-adic valuation. Let up be the sign reduction
modulo p defined as up (x)= x if 0≤ x≤ p/2 and up (x)= p− x if p/2< x< p. We say that a …

We present an evolutionary self-governing model based on the numerical atomic rule Z (a,
b)= ab/gcd (a, b) 2, for a, b positive integers. Starting with a sequence of numbers, the initial …

Si une suite bidimensionnelle récurrente avec conditions initiales définies par substitution
linéaire et une suite bidimensionnelle engendrée par substitution plane sont identiques sur …

The author used the automatic proof procedure introduced in and verified that the 4096
homomorphic recurrent double sequences with constant borders defined over Klein's …

A recurrent 2-dimensional sequence a (m, n) is given by fixing particular sequences a (m, 0),
a (0, n) as initial conditions and a rule of recurrence a (m, n)= f (a (m, n− 1), a (m− 1, n− 1), a …

According to a classical result of E. Kummer, the p-adic valuation vp applied to a binomial
coefficient (a+ ba) yields the number of carries occurring while adding a and b in basis p. We …

The concept of the order of a 2-sequence is introduced in this paper. The order of a 2-
sequence is a natural but not trivial extension of the order of one-dimensional (1D) linear …

Abstract A recurrent 2-dimensional (double) sequence t (m, n) is given by fixing particular
sequences t (m, 0), t (0, n) as initial conditions and a rule of recurrence t (m, n)= f (t (m, n− 1) …

The importance of hiding information when transferring data has been highlighted since the
early days of communication. Even though initially information hiding was mainly used in …

Abstract If v1,..., vm are lexicographically positive elements in Zn, a general recurrence is a
computation rule a (x)= f (a (x− v1),..., a (x− vm)). Let H be a finite abelian p-group, h: Hm→ H …