The density of 0's in recurrence double sequences

Yossi Moshe

doi:10.1016/S0022-314X(03)00103-3

The density of 0's in recurrence double sequences

Yossi Moshe

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let A = (A(i,j))_i=0,j=-∞^∞,∞ be a double sequence over a finite field F = GF(q) satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of F, we show how to obtain an explicit formula for the number of g's in the first qⁿ rows of A. We also characterize the cases when the density of 0's is 1.

Original language	English
Pages (from-to)	109-121
Number of pages	13
Journal	Journal of Number Theory
Volume	103
Issue number	1
DOIs	https://doi.org/10.1016/S0022-314X(03)00103-3
State	Published - 1 Jan 2003

Keywords

Asymptotic frequency
Cellular automata
Pascal's triangle
Polynomial recurrence

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0022-314X(03)00103-3

Cite this

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abstract = "Let A = (A(i,j))i=0,j=-∞∞,∞ be a double sequence over a finite field F = GF(q) satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of F, we show how to obtain an explicit formula for the number of g's in the first qn rows of A. We also characterize the cases when the density of 0's is 1.",

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N2 - Let A = (A(i,j))i=0,j=-∞∞,∞ be a double sequence over a finite field F = GF(q) satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of F, we show how to obtain an explicit formula for the number of g's in the first qn rows of A. We also characterize the cases when the density of 0's is 1.

AB - Let A = (A(i,j))i=0,j=-∞∞,∞ be a double sequence over a finite field F = GF(q) satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of F, we show how to obtain an explicit formula for the number of g's in the first qn rows of A. We also characterize the cases when the density of 0's is 1.

KW - Asymptotic frequency

KW - Cellular automata

KW - Pascal's triangle

KW - Polynomial recurrence

UR - https://www.scopus.com/pages/publications/0242508558

U2 - 10.1016/S0022-314X(03)00103-3

DO - 10.1016/S0022-314X(03)00103-3

M3 - Article

AN - SCOPUS:0242508558

SN - 0022-314X

VL - 103

SP - 109

EP - 121

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

The density of 0's in recurrence double sequences

Abstract

Keywords

ASJC Scopus subject areas

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