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Posets :: maximalChains

maximalChains -- returns all maximal chains of a poset

Synopsis

Description

The maximal chains of P are totally orders subsets of P which are not properly contained in any other totally ordered subsets.

This method returns a list of all maximal chains. The maximal chains are themselves lists of elements in P ordered from smallest to largest.

The results of this method are cached.

i1 : S = QQ[a,b,c];
i2 : P = divisorPoset(a*b^2*c);
i3 : C = maximalChains P

                   2      2                          2                      
o3 = {{1, c, b*c, b c, a*b c}, {1, c, b*c, a*b*c, a*b c}, {1, c, a*c, a*b*c,
     ------------------------------------------------------------------------
        2                 2      2                          2            2 
     a*b c}, {1, b, b*c, b c, a*b c}, {1, b, b*c, a*b*c, a*b c}, {1, b, b ,
     ------------------------------------------------------------------------
      2      2            2     2     2                          2          
     b c, a*b c}, {1, b, b , a*b , a*b c}, {1, b, a*b, a*b*c, a*b c}, {1, b,
     ------------------------------------------------------------------------
             2     2                          2                          2   
     a*b, a*b , a*b c}, {1, a, a*c, a*b*c, a*b c}, {1, a, a*b, a*b*c, a*b c},
     ------------------------------------------------------------------------
                    2     2
     {1, a, a*b, a*b , a*b c}}

o3 : List

Ways to use maximalChains :

  • maximalChains(Poset)