On subword decomposition and balanced polynomials |
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Authors: | Yossi Moshe |
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Institution: | CNRS, LRI, Université Paris Sud, Orsay, France |
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Abstract: | Let H(x) be a monic polynomial over a finite field F=GF(q). Denote by Na(n) the number of coefficients in Hn which are equal to an element a∈F, and by G the set of elements a∈F× such that Na(n)>0 for some n. We study the relationship between the numbers (Na(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 Na(n)≈Nb(n), a,b∈G. 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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Keywords: | primary 11B85 11C08 secondary 11B05 11B50 11B73 11B65 |
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