Inequalities for the Crank

Bülent Ekin A.

Journal of Combinatorial Theory. Series A, vol.83, no.2, pp.283-289, 1998 (SCI-Expanded) identifier


Garvan first defined certain "vector partitions" and assigned to each such partition a "rank." Denoting byNV(r,m,n) the (weighted) count of the vector partitions ofnwith rankrmodulom, he gave a number of relations between the numbersNV(r,m,mn+k) whenm=5, 7 and 11, 0≤r,k