On subword decomposition and balanced polynomials Original Research Article

Let H(x) be a monic polynomial over a finite field image. Denote by image the number of coefficients in Hn which are equal to an element image, and by G the set of elements image such that image for some n. We study the relationship between the numbers image and the patterns in the base q representation of n. This enables us to prove that for “most” nʹs we have image, a,bset membership, variantG. Considering the case H=x+1, we provide new results on Pascalʹs triangle modulo a prime. We also provide analogous results for the triangle of Stirling numbers of the first kind.