> > V1:=vecptnsC(4,1,5); V1 := [[[], [], [1, 1, 1, 1]], [[], [1, 1], [2]], [[], [1, 2], [1]], [[], [4], []], [[1], [1, 1], [1]], [[1], [3], []], [[2], [2], []], [[1, 2], [1], []], [[3], [1], []]] > nops(V1); 9 > add(vpw(V1[i]),i=1..nops(V1)); 1 > > # There are 9 vector partitions of 4 with crank = 1 mod 5 > # and total weight = 1. > > # vector partitions of 4 with crank = 2 mod 5 > > V2:=vecptnsC(4,2,5); V2 := [[[], [], [1, 1, 2]], [[], [1, 1, 1], [1]], [[], [2, 2], []], [[], [1, 3], []], [[1], [], [1, 1, 1]], [[1], [1, 2], []], [[2], [1, 1], []]] > nops(V2); 7 > add(vpw(V2[i]),i=1..nops(V2)); 1 > > # There are 7 vector partitions of 4 with crank = 0 mod 5 > # and total weight = 1. > > # vector partitions of 4 with crank = 3 mod 5 > > V3:=vecptnsC(4,3,5); V3 := [[[], [], [2, 2]], [[], [], [1, 3]], [[], [1], [1, 1, 1]], [[], [1, 1, 2], []], [[1], [], [1, 2]], [[1], [1, 1, 1], []], [[2], [], [1, 1]]] > nops(V3); 7 > add(vpw(V3[i]),i=1..nops(V3)); 1 > > # There are 7 vector partitions of 4 with crank = 3 mod 5 > # and total weight = 1. > > # vector partitions of 4 with crank = 4 mod 5 > > V4:=vecptnsC(4,4,5); V4 := [[[], [], [4]], [[], [1], [1, 2]], [[], [2], [1, 1]], [[], [1, 1, 1, 1], []], [[1], [], [3]], [[1], [1], [1, 1]], [[2], [], [2]], [[1, 2], [], [1]], [[3], [], [1]]]