- FindStat

Identifier

St001171: Permutations ⟶ ℤ (values match St000055The inversion sum of a permutation.)

Values

=>
                            
                            
                            
                            

                        [1]=>0
[1,2]=>0
[2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>3
[3,1,2]=>3
[3,2,1]=>4
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>4
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>3
[2,3,4,1]=>6
[2,4,1,3]=>5
[2,4,3,1]=>7
[3,1,2,4]=>3
[3,1,4,2]=>5
[3,2,1,4]=>4
[3,2,4,1]=>7
[3,4,1,2]=>8
[3,4,2,1]=>9
[4,1,2,3]=>6
[4,1,3,2]=>7
[4,2,1,3]=>7
[4,2,3,1]=>9
[4,3,1,2]=>9
[4,3,2,1]=>10
                    

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Description

The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$.

References

[1] Iyama, O., Zhang, X. Classifying τ-tilting modules over the Auslander algebra of $K[x]/(x^n)$ arXiv:1602.05037

Created

Apr 30, 2018 at 17:08 by Rene Marczinzik

Updated

May 02, 2018 at 11:21 by Rene Marczinzik