Recall that a P-partition for a naturally labeled poset P on vertices 1, ..., n is a function f: P →NN which is order-reversing, i.e., if i < j in P then f(i) ≥f(j) in NN. To a P-partition f we can assign the monomial t1f(1) ...tnf(n). The P-partition ring is the ring spanned by the monomials corresponding to P-partitions.
i1 : P = poset {{1,2}, {2,4}, {3,4}, {3,5}}; |
i2 : pPartitionRing P QQ[t , t , t , t , t , t ] {3} {3, 4} {0} {0, 1} {0, 1, 2, 3} {0, 1, 2, 3, 4} o2 = ----------------------------------------------------------------- t t - t t {3, 4} {0, 1, 2, 3} {3} {0, 1, 2, 3, 4} o2 : QuotientRing |
i3 : pPartitionRing(divisorPoset 6, Strategy => "4ti2") using temporary file name /tmp/M2-17196-0/0 QQ[t , t , t , t , t ] {0} {0, 1} {0, 2} {0, 1, 2} {0, 1, 2, 3} o3 = ----------------------------------------------------- t t - t t {0, 1} {0, 2} {0} {0, 1, 2} o3 : QuotientRing |