TY - GEN A1 - Averkov, Gennadiy A1 - Bey, Christian T1 - Description of polygonal regions by polynomials of bounded degree T2 - Monatshefte für Mathematik N2 - 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. KW - Gray code KW - Polygon KW - Polynomial KW - Semi-algebraic set KW - Theorem of Bröcker and Scheiderer Y1 - 2011 U6 - https://doi.org/10.1007/s00605-010-0224-x SN - 1436-5081 VL - 162 IS - 1 SP - 19 EP - 27 ER -