In this paper we examine Ehrenfeucht-Fräıssé (EF) games on fields and vector spaces. We find the exact length of the EF game on two algebraically closed fields of finite transcendence degree over Q or Z/pZ. We also determine an upper bound on the length of any EF game on models (F1 ,F1) and (F m 2 ,F2 of vector spaces where m = n and a lower bound for the special case F1 = F2.

In 1977 G.P. Thomas has shown that the sequence of Schur polynomials associated to a partition can be comfortabely generated from the sequence of variables x = (x1; x2; x3; : : :) by the application of a mixed shift/multiplication operator, which in turn can be easily computed from the set SY T () of standard Young tableaux of shape. We generalise this construction, thereby making possible | fo...