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On subword decomposition and balanced polynomials

✍ Scribed by Yossi Moshe

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
207 KB
Volume
123
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let H (x) be a monic polynomial over a finite field F = GF(q). Denote by N a (n) the number of coefficients in H n which are equal to an element a ∈ F, and by G the set of elements a ∈ F × such that N a (n) > 0 for some n. We study the relationship between the numbers (N a (n)) a∈G and the patterns in the base q representation of n. This enables us to prove that for "most" n's we have

Considering the case H = x + 1, we provide new results on Pascal's triangle modulo a prime. We also provide analogous results for the triangle of Stirling numbers of the first kind.

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