FUNCTION: partitions[ptnSCHUR] - Schur partitions CALLING SEQUENCE: ptnSCHUR(ptn) PARAMETERS: ptn - partition GLOBAL VARIABLES: NONE SYNOPSIS: Returns true if ptn is a partition in which difference between parts is at least 3 and such that no two consecutive multiples of 3 occur as parts EXAMPLES: > with(combinat): > with(partitions): > with(qseries): > ptns:=partition(8): > ptns1:=select(ptnSCHUR,ptns); ptns1 := [[2, 6], [1, 7], [8]] > ptns2:=select(ptn-> if convert(modp(ptn,6),set) subset {1,5} then true else false fi, ptns); ptns2 := [[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 5], [1, 7]] > nops(ptns), nops(ptns1), nops(ptns2); 22, 3, 3 DISCUSSION: There are 22 partitions of 8. Of these 3 satisfy the condition (listed) We also find the partitions of 8 with parts congruent to 1 or 5 mod 6. SEE ALSO: PSCHUR