# What is a fewnomial?

I came across the theory of "fewnomials" (by Khovanskii), which (I guess) are related to polynomials. However, I was surprised that there is no single question on stackexchange concerning fewnomials, and few in mathematical research in general (there are some papers on arXiv). Does anyone know something more about the concept and can please explain me the idea behind fewnomials? Thanks.

• i believe polynomial where only very few coefficients are nonzero, e.g. $x^{13} - x - 1 = 0$ – abel Feb 1 '15 at 20:28
• Dunno, but clearly they ought to have been named oligonomials! – Brian M. Scott Feb 1 '15 at 20:31
• @BrianM.Scott Why oligonomials? btw. in arxiv.org/pdf/1412.4548.pdf they say that they can be called also "sparse" or "lacunary" polynomials. – pisoir Feb 1 '15 at 20:37
• Khovanskii generalized Descartes bounds on the number of real roots of a polynomial to systems of multivariate polynomial equations. The bounds are useful primarily for polynomials with few monomials "fewnomials". A web search should turn up many expositions (besides Khovanskii's book). – Bill Dubuque Feb 1 '15 at 20:43
• It's a nomial that has an unpleasant odor. Compare en.wikipedia.org/wiki/Pep%C3%A9_Le_Pew – Will Jagy Feb 1 '15 at 21:23