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Common terms in binary recurrences

Erzsébet Orosz (2006)

Acta Mathematica Universitatis Ostraviensis

The purpose of this paper is to prove that the common terms of linear recurrences M ( 2 a , - 1 , 0 , b ) and N ( 2 c , - 1 , 0 , d ) have at most 2 common terms if p = 2 , and have at most three common terms if p > 2 where D and p are fixed positive integers and p is a prime, such that neither D nor D + p is perfect square, further a , b , c , d are nonzero integers satisfying the equations a 2 - D b 2 = 1 and c 2 - ( D + p ) d 2 = 1 .

Convolution of second order linear recursive sequences II.

Tamás Szakács (2017)

Communications in Mathematics

We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

Counting Maximal Distance-Independent Sets in Grid Graphs

Reinhardt Euler, Paweł Oleksik, Zdzisław Skupień (2013)

Discussiones Mathematicae Graph Theory

Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied

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