randomShellableIdealChain -- Produces a chain of ideals from a random shelling

Synopsis

• Usage:

  L = randomShellableIdealChain(R,m,k)

  L = randomShellableIdealChain(R,m)

• Inputs:
  • R, a ring, a polynomial ring
  • m, an integer, dimension of the facets in the shellable complex
  • k, an integer, the degree of the smallest ideal
• Outputs:
  • L, a list, list of Stanley-Riesner ideals of the simplicial complexes of the truncations of the shelling.

Description

i1 : R = ZZ/101[x_0..x_3];

i2 : L = randomShellableIdealChain(R,1)

o2 = {monomialIdeal (x , x ), monomialIdeal (x , x x ), monomialIdeal (x x ,
                      0   1                   0   1 2                   0 1 
     ------------------------------------------------------------------------
     x x , x x ), monomialIdeal (x x , x x , x x x ), monomialIdeal (x x ,
      0 2   1 2                   0 1   0 2   1 2 3                   0 2 
     ------------------------------------------------------------------------
     x x x , x x x ), monomialIdeal (x x x , x x x , x x x , x x x )}
      0 1 3   1 2 3                   0 1 2   0 1 3   0 2 3   1 2 3

o2 : List

Caveat

See also

• randomShelling -- produces a random chain of shellable complexes
• idealFromShelling -- Produces an ideal from a shelling
• idealChainFromShelling -- Produces chains of ideals from a shelling.
• randomShellableIdeal -- Produces a ideal from a random shellable simplicial complex