A Characteristic Factor for the 3-Term IP Roth Theorem in Z(3)(N)

作者：McCutcheon Randall^*; Windsor Alistair

来源：Electronic Journal of Combinatorics, 2014, 21(3): P3.3.

Let Omega = circle plus(i=1)infinity Z(3) and e(i) = (0,..., 0, 1, 0,...) where the 1 occurs in the i-th coordinate. Let F = {alpha subset of N : phi not equal alpha, alpha is finite}. There is a natural inclusion of F into Omega where alpha is an element of F is mapped to e(alpha) = Sigma(i is an element of alpha) e(i). We give a new proof that if E subset of Omega with d*(E) %26gt; 0 then there exist omega is an element of Omega and alpha is an element of F such that %26lt;br%26gt;{omega, omega + e(alpha), omega + 2e(alpha)} subset of E. %26lt;br%26gt;Our proof establishes that for the ergodic reformulation of the problem there is a characteristic factor that is a one step compact extension of the Kronecker factor.

• 出版日期2014-7-3