Quotients of Dilworth truncations (Q1101458)

Sufficient conditions are given for an elementary quotient of the k-th Dilworth truncation of a matroid M to be the k-th Dilworth truncation of a quotient of M. As special cases, contractions of Dilworth truncations and principal truncations by connected flats of Dilworth truncations are characterised as Dilworth truncations of certain matroids. As an application of the theory it is shown that the degree of the minimal extension field of GF(q) needed to represent the first Dilworth truncation of PG(r-1,q) is greater than 2r-4.