@misc{AverkovBey, author = {Averkov, Gennadiy and Bey, Christian}, title = {Description of polygonal regions by polynomials of bounded degree}, series = {Monatshefte f{\"u}r Mathematik}, volume = {162}, journal = {Monatshefte f{\"u}r Mathematik}, number = {1}, issn = {1436-5081}, doi = {10.1007/s00605-010-0224-x}, pages = {19 -- 27}, abstract = {We show that every (possibly unbounded) convex polygon P in R2 with m edges can be represented by inequalities p 1 ≥ 0, . . ., p n ≥ 0, where the p i 's are products of at most k affine functions each vanishing on an edge of P and n = n(m, k) satisfies s(m,k)≤n(m,k)≤(1+εm)s(m,k) with s(m,k) ≔ max {m/k, log2 m} and εm→0 as m→∞. This choice of n is asymptotically best possible. An analogous result on representing the interior of P in the form p 1 > 0, . . ., p n > 0 is also given. For k ≤ m/log2 m these statements remain valid for representations with arbitrary polynomials of degree not exceeding k.}, language = {en} }