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") ------------------------------------------------- 4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team. 4ti2 comes with ABSOLUTELY NO WARRANTY. This is free software, and you are welcome to redistribute it under certain conditions. For details, see the file COPYING. ------------------------------------------------- Using 64 bit integers. 4ti2 Total Time: 0.00 secs. using temporary file name /tmp/M2-3867-0/0 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 |