- FindStat

Identifier

St001432: Integer partitions ⟶ ℤ (values match St000783The side length of the largest staircase partition fitting into a partition.)

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [1]=>1
[2]=>1
[1,1]=>1
[3]=>1
[2,1]=>2
[1,1,1]=>1
[4]=>1
[3,1]=>2
[2,2]=>2
[2,1,1]=>2
[1,1,1,1]=>1
[5]=>1
[4,1]=>2
[3,2]=>2
[3,1,1]=>2
[2,2,1]=>2
[2,1,1,1]=>2
[1,1,1,1,1]=>1
[6]=>1
[5,1]=>2
[4,2]=>2
[4,1,1]=>2
[3,3]=>2
[3,2,1]=>3
[3,1,1,1]=>2
[2,2,2]=>2
[2,2,1,1]=>2
[2,1,1,1,1]=>2
[1,1,1,1,1,1]=>1
[7]=>1
[6,1]=>2
[5,2]=>2
[5,1,1]=>2
[4,3]=>2
[4,2,1]=>3
[4,1,1,1]=>2
[3,3,1]=>3
[3,2,2]=>3
[3,2,1,1]=>3
[3,1,1,1,1]=>2
[2,2,2,1]=>2
[2,2,1,1,1]=>2
[2,1,1,1,1,1]=>2
[1,1,1,1,1,1,1]=>1
[8]=>1
[7,1]=>2
[6,2]=>2
[6,1,1]=>2
[5,3]=>2
[5,2,1]=>3
[5,1,1,1]=>2
[4,4]=>2
[4,3,1]=>3
[4,2,2]=>3
[4,2,1,1]=>3
[4,1,1,1,1]=>2
[3,3,2]=>3
[3,3,1,1]=>3
[3,2,2,1]=>3
[3,2,1,1,1]=>3
[3,1,1,1,1,1]=>2
[2,2,2,2]=>2
[2,2,2,1,1]=>2
[2,2,1,1,1,1]=>2
[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1]=>1
[9]=>1
[8,1]=>2
[7,2]=>2
[7,1,1]=>2
[6,3]=>2
[6,2,1]=>3
[6,1,1,1]=>2
[5,4]=>2
[5,3,1]=>3
[5,2,2]=>3
[5,2,1,1]=>3
[5,1,1,1,1]=>2
[4,4,1]=>3
[4,3,2]=>3
[4,3,1,1]=>3
[4,2,2,1]=>3
[4,2,1,1,1]=>3
[4,1,1,1,1,1]=>2
[3,3,3]=>3
[3,3,2,1]=>3
[3,3,1,1,1]=>3
[3,2,2,2]=>3
[3,2,2,1,1]=>3
[3,2,1,1,1,1]=>3
[3,1,1,1,1,1,1]=>2
[2,2,2,2,1]=>2
[2,2,2,1,1,1]=>2
[2,2,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1]=>1
[10]=>1
[9,1]=>2
[8,2]=>2
[8,1,1]=>2
[7,3]=>2
[7,2,1]=>3
[7,1,1,1]=>2
[6,4]=>2
[6,3,1]=>3
[6,2,2]=>3
[6,2,1,1]=>3
[6,1,1,1,1]=>2
[5,5]=>2
[5,4,1]=>3
[5,3,2]=>3
[5,3,1,1]=>3
[5,2,2,1]=>3
[5,2,1,1,1]=>3
[5,1,1,1,1,1]=>2
[4,4,2]=>3
[4,4,1,1]=>3
[4,3,3]=>3
[4,3,2,1]=>4
[4,3,1,1,1]=>3
[4,2,2,2]=>3
[4,2,2,1,1]=>3
[4,2,1,1,1,1]=>3
[4,1,1,1,1,1,1]=>2
[3,3,3,1]=>3
[3,3,2,2]=>3
[3,3,2,1,1]=>3
[3,3,1,1,1,1]=>3
[3,2,2,2,1]=>3
[3,2,2,1,1,1]=>3
[3,2,1,1,1,1,1]=>3
[3,1,1,1,1,1,1,1]=>2
[2,2,2,2,2]=>2
[2,2,2,2,1,1]=>2
[2,2,2,1,1,1,1]=>2
[2,2,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1]=>1
[11]=>1
[10,1]=>2
[9,2]=>2
[9,1,1]=>2
[8,3]=>2
[8,2,1]=>3
[8,1,1,1]=>2
[7,4]=>2
[7,3,1]=>3
[7,2,2]=>3
[7,2,1,1]=>3
[7,1,1,1,1]=>2
[6,5]=>2
[6,4,1]=>3
[6,3,2]=>3
[6,3,1,1]=>3
[6,2,2,1]=>3
[6,2,1,1,1]=>3
[6,1,1,1,1,1]=>2
[5,5,1]=>3
[5,4,2]=>3
[5,4,1,1]=>3
[5,3,3]=>3
[5,3,2,1]=>4
[5,3,1,1,1]=>3
[5,2,2,2]=>3
[5,2,2,1,1]=>3
[5,2,1,1,1,1]=>3
[5,1,1,1,1,1,1]=>2
[4,4,3]=>3
[4,4,2,1]=>4
[4,4,1,1,1]=>3
[4,3,3,1]=>4
[4,3,2,2]=>4
[4,3,2,1,1]=>4
[4,3,1,1,1,1]=>3
[4,2,2,2,1]=>3
[4,2,2,1,1,1]=>3
[4,2,1,1,1,1,1]=>3
[4,1,1,1,1,1,1,1]=>2
[3,3,3,2]=>3
[3,3,3,1,1]=>3
[3,3,2,2,1]=>3
[3,3,2,1,1,1]=>3
[3,3,1,1,1,1,1]=>3
[3,2,2,2,2]=>3
[3,2,2,2,1,1]=>3
[3,2,2,1,1,1,1]=>3
[3,2,1,1,1,1,1,1]=>3
[3,1,1,1,1,1,1,1,1]=>2
[2,2,2,2,2,1]=>2
[2,2,2,2,1,1,1]=>2
[2,2,2,1,1,1,1,1]=>2
[2,2,1,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1]=>1
[12]=>1
[11,1]=>2
[10,2]=>2
[10,1,1]=>2
[9,3]=>2
[9,2,1]=>3
[9,1,1,1]=>2
[8,4]=>2
[8,3,1]=>3
[8,2,2]=>3
[8,2,1,1]=>3
[8,1,1,1,1]=>2
[7,5]=>2
[7,4,1]=>3
[7,3,2]=>3
[7,3,1,1]=>3
[7,2,2,1]=>3
[7,2,1,1,1]=>3
[7,1,1,1,1,1]=>2
[6,6]=>2
[6,5,1]=>3
[6,4,2]=>3
[6,4,1,1]=>3
[6,3,3]=>3
[6,3,2,1]=>4
[6,3,1,1,1]=>3
[6,2,2,2]=>3
[6,2,2,1,1]=>3
[6,2,1,1,1,1]=>3
[6,1,1,1,1,1,1]=>2
[5,5,2]=>3
[5,5,1,1]=>3
[5,4,3]=>3
[5,4,2,1]=>4
[5,4,1,1,1]=>3
[5,3,3,1]=>4
[5,3,2,2]=>4
[5,3,2,1,1]=>4
[5,3,1,1,1,1]=>3
[5,2,2,2,1]=>3
[5,2,2,1,1,1]=>3
[5,2,1,1,1,1,1]=>3
[5,1,1,1,1,1,1,1]=>2
[4,4,4]=>3
[4,4,3,1]=>4
[4,4,2,2]=>4
[4,4,2,1,1]=>4
[4,4,1,1,1,1]=>3
[4,3,3,2]=>4
[4,3,3,1,1]=>4
[4,3,2,2,1]=>4
[4,3,2,1,1,1]=>4
[4,3,1,1,1,1,1]=>3
[4,2,2,2,2]=>3
[4,2,2,2,1,1]=>3
[4,2,2,1,1,1,1]=>3
[4,2,1,1,1,1,1,1]=>3
[4,1,1,1,1,1,1,1,1]=>2
[3,3,3,3]=>3
[3,3,3,2,1]=>3
[3,3,3,1,1,1]=>3
[3,3,2,2,2]=>3
[3,3,2,2,1,1]=>3
[3,3,2,1,1,1,1]=>3
[3,3,1,1,1,1,1,1]=>3
[3,2,2,2,2,1]=>3
[3,2,2,2,1,1,1]=>3
[3,2,2,1,1,1,1,1]=>3
[3,2,1,1,1,1,1,1,1]=>3
[3,1,1,1,1,1,1,1,1,1]=>2
[2,2,2,2,2,2]=>2
[2,2,2,2,2,1,1]=>2
[2,2,2,2,1,1,1,1]=>2
[2,2,2,1,1,1,1,1,1]=>2
[2,2,1,1,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1,1]=>1
                    

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Description

The order dimension of the partition.
Given a partition $\lambda$, let $I(\lambda)$ be the principal order ideal in the Young lattice generated by $\lambda$. The order dimension of a partition is defined as the order dimension of the poset $I(\lambda)$.

Code

def statistic(p):
    return posets.YoungsLatticePrincipalOrderIdeal(p).join_irreducibles_poset().width()

Created

Jun 22, 2019 at 09:23 by Rene Marczinzik

Updated

Feb 26, 2023 at 16:46 by Martin Rubey