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youngSubposet -- generates a subposet of Young's lattice

Description

Young's lattice is the infinite lattice of all partitions with partial ordering given by componentwise linear ordering.

If $n$ is specified, then the poset returned is the subposet of Young's lattice given by the induced subposet of all partitions of size at most $n$.

i1 : youngSubposet 4

o1 = Relation Matrix: | 1 1 1 1 1 1 1 1 1 1 1 1 |
                      | 0 1 1 1 1 1 1 1 1 1 1 1 |
                      | 0 0 1 0 1 1 0 1 1 1 1 0 |
                      | 0 0 0 1 0 1 1 0 1 1 1 1 |
                      | 0 0 0 0 1 0 0 1 1 0 0 0 |
                      | 0 0 0 0 0 1 0 0 1 1 1 0 |
                      | 0 0 0 0 0 0 1 0 0 0 1 1 |
                      | 0 0 0 0 0 0 0 1 0 0 0 0 |
                      | 0 0 0 0 0 0 0 0 1 0 0 0 |
                      | 0 0 0 0 0 0 0 0 0 1 0 0 |
                      | 0 0 0 0 0 0 0 0 0 0 1 0 |
                      | 0 0 0 0 0 0 0 0 0 0 0 1 |

o1 : Poset

If an upper partition, hi, is specified, then the returned poset is the closedInterval of the Young's lattice between lo and hi, where lo either is the empty partition or is specified.

i2 : youngSubposet({3,1}, {4,2,1})

o2 = Relation Matrix: | 1 1 1 1 1 1 1 1 |
                      | 0 1 0 1 0 1 0 1 |
                      | 0 0 1 1 0 0 1 1 |
                      | 0 0 0 1 0 0 0 1 |
                      | 0 0 0 0 1 1 1 1 |
                      | 0 0 0 0 0 1 0 1 |
                      | 0 0 0 0 0 0 1 1 |
                      | 0 0 0 0 0 0 0 1 |

o2 : Poset

See also

Ways to use youngSubposet:

  • youngSubposet(List)
  • youngSubposet(List,List)
  • youngSubposet(ZZ)

For the programmer

The object youngSubposet is a method function.

The source of this document is in Posets.m2:3994:0.