Congruences for a restricted m-ary partition function

We discuss a family of restricted m-ary partition functions b(m,j)(n), which is the number of m-ary partitions of n with at most i + j copies of the part m(i) allowed. We then use generating function dissections to prove the following family of congruences for k greater than or equal to 2 and 1 less than or equal to t less than or equal to m - k + 1: b(m,m - 1) (m(k+t)n + m(k+t-1) + m(k+t-2) + ... + m(k)) drop 0 (mod 2(t-1)k). (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 05A17; 11P83.