- FindStat

Identifier

St001235: Integer compositions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>1
[1,1]=>2
[2]=>1
[1,1,1]=>3
[1,2]=>2
[2,1]=>2
[3]=>1
[1,1,1,1]=>4
[1,1,2]=>3
[1,2,1]=>2
[1,3]=>2
[2,1,1]=>3
[2,2]=>2
[3,1]=>2
[4]=>1
[1,1,1,1,1]=>5
[1,1,1,2]=>4
[1,1,2,1]=>3
[1,1,3]=>3
[1,2,1,1]=>3
[1,2,2]=>2
[1,3,1]=>2
[1,4]=>2
[2,1,1,1]=>4
[2,1,2]=>3
[2,2,1]=>2
[2,3]=>2
[3,1,1]=>3
[3,2]=>2
[4,1]=>2
[5]=>1
[1,1,1,1,1,1]=>6
[1,1,1,1,2]=>5
[1,1,1,2,1]=>4
[1,1,1,3]=>4
[1,1,2,1,1]=>3
[1,1,2,2]=>3
[1,1,3,1]=>3
[1,1,4]=>3
[1,2,1,1,1]=>4
[1,2,1,2]=>3
[1,2,2,1]=>2
[1,2,3]=>2
[1,3,1,1]=>3
[1,3,2]=>2
[1,4,1]=>2
[1,5]=>2
[2,1,1,1,1]=>5
[2,1,1,2]=>4
[2,1,2,1]=>3
[2,1,3]=>3
[2,2,1,1]=>3
[2,2,2]=>2
[2,3,1]=>2
[2,4]=>2
[3,1,1,1]=>4
[3,1,2]=>3
[3,2,1]=>2
[3,3]=>2
[4,1,1]=>3
[4,2]=>2
[5,1]=>2
[6]=>1
                    

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Description

The global dimension of the corresponding Comp-Nakayama algebra.
We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".

Created

Jul 30, 2018 at 20:58 by Rene Marczinzik

Updated

Jul 30, 2018 at 20:58 by Rene Marczinzik