A lattice path approach to counting partitions with minimum rank

In this paper, we give a combinatorial proof via lattice paths of the following result due to Andrews and Bressoud: for t⩽1, the number of partitions of n with all successive ranks at least t is equal to the number of partitions of n with no part of size 2−t. The identity is a special case of a more general theorem proved by Andrews and Bressoud using a sieve.