plueckerPoset -- computes a poset associated to the Plücker relations

Synopsis

Usage:

P = plueckerPoset n
Inputs:
- n, an integer, the size of the set to partition
Outputs:
- P, an instance of the type Poset,

Description

The ideal of Plücker relations has a quadratic Groebner basis. Under a suitable term order, the incomparable pairs of the poset $P$ generate the initial ideal of the ideal of Plücker relations.

Given two subsets $S$ and $T$ of ${0,\ldots,n-1}$, we partially order $S \leq T$ if $\#S \geq \#T$ and $S_i \leq T_i$ for all $i$ from $1$ to $\#T$.

i1 : P = plueckerPoset 4;

i2 : coveringRelations P

o2 = {{{0}, {1}}, {{1}, {2}}, {{0, 1}, {0, 2}}, {{2}, {3}}, {{0, 2}, {0, 3}},
     ------------------------------------------------------------------------
     {{0, 2}, {1, 2}}, {{1, 2}, {1, 3}}, {{0, 1, 2}, {0, 1, 3}}, {{3}, {}},
     ------------------------------------------------------------------------
     {{0, 3}, {0}}, {{0, 3}, {1, 3}}, {{1, 3}, {2, 3}}, {{1, 3}, {1}}, {{0,
     ------------------------------------------------------------------------
     1, 3}, {0, 2, 3}}, {{0, 1, 3}, {0, 1}}, {{2, 3}, {2}}, {{0, 2, 3}, {0,
     ------------------------------------------------------------------------
     2}}, {{0, 2, 3}, {1, 2, 3}}, {{1, 2, 3}, {1, 2}}, {{0, 1, 2, 3}, {0, 1,
     ------------------------------------------------------------------------
     2}}}

o2 : List

Ways to use plueckerPoset :

plueckerPoset(ZZ)

For the programmer

The object plueckerPoset is a method function.