- FindStat

Identifier

St000967: Dyck paths ⟶ ℤ

Values

[1,0] => 3

[1,0,1,0] => 4

[1,1,0,0] => 4

[1,0,1,0,1,0] => 5

[1,0,1,1,0,0] => 5

[1,1,0,0,1,0] => 5

[1,1,0,1,0,0] => 4

[1,1,1,0,0,0] => 5

[1,0,1,0,1,0,1,0] => 6

[1,0,1,0,1,1,0,0] => 6

[1,0,1,1,0,0,1,0] => 6

[1,0,1,1,0,1,0,0] => 4

[1,0,1,1,1,0,0,0] => 6

[1,1,0,0,1,0,1,0] => 6

[1,1,0,0,1,1,0,0] => 6

[1,1,0,1,0,0,1,0] => 4

[1,1,0,1,0,1,0,0] => 4

[1,1,0,1,1,0,0,0] => 4

[1,1,1,0,0,0,1,0] => 6

[1,1,1,0,0,1,0,0] => 4

[1,1,1,0,1,0,0,0] => 4

[1,1,1,1,0,0,0,0] => 6

[1,0,1,0,1,0,1,0,1,0] => 7

[1,0,1,0,1,0,1,1,0,0] => 7

[1,0,1,0,1,1,0,0,1,0] => 7

[1,0,1,0,1,1,0,1,0,0] => 4

[1,0,1,0,1,1,1,0,0,0] => 7

[1,0,1,1,0,0,1,0,1,0] => 7

[1,0,1,1,0,0,1,1,0,0] => 7

[1,0,1,1,0,1,0,0,1,0] => 3

[1,0,1,1,0,1,0,1,0,0] => 4

[1,0,1,1,0,1,1,0,0,0] => 3

[1,0,1,1,1,0,0,0,1,0] => 7

[1,0,1,1,1,0,0,1,0,0] => 4

[1,0,1,1,1,0,1,0,0,0] => 3

[1,0,1,1,1,1,0,0,0,0] => 7

[1,1,0,0,1,0,1,0,1,0] => 7

[1,1,0,0,1,0,1,1,0,0] => 7

[1,1,0,0,1,1,0,0,1,0] => 7

[1,1,0,0,1,1,0,1,0,0] => 4

[1,1,0,0,1,1,1,0,0,0] => 7

[1,1,0,1,0,0,1,0,1,0] => 4

[1,1,0,1,0,0,1,1,0,0] => 4

[1,1,0,1,0,1,0,0,1,0] => 4

[1,1,0,1,0,1,0,1,0,0] => 3

[1,1,0,1,0,1,1,0,0,0] => 4

[1,1,0,1,1,0,0,0,1,0] => 4

[1,1,0,1,1,0,0,1,0,0] => 0

[1,1,0,1,1,0,1,0,0,0] => 3

[1,1,0,1,1,1,0,0,0,0] => 4

[1,1,1,0,0,0,1,0,1,0] => 7

[1,1,1,0,0,0,1,1,0,0] => 7

[1,1,1,0,0,1,0,0,1,0] => 3

[1,1,1,0,0,1,0,1,0,0] => 4

[1,1,1,0,0,1,1,0,0,0] => 3

[1,1,1,0,1,0,0,0,1,0] => 3

[1,1,1,0,1,0,0,1,0,0] => 3

[1,1,1,0,1,0,1,0,0,0] => 3

[1,1,1,0,1,1,0,0,0,0] => 3

[1,1,1,1,0,0,0,0,1,0] => 7

[1,1,1,1,0,0,0,1,0,0] => 4

[1,1,1,1,0,0,1,0,0,0] => 3

[1,1,1,1,0,1,0,0,0,0] => 4

[1,1,1,1,1,0,0,0,0,0] => 7

[1,0,1,0,1,0,1,0,1,0,1,0] => 8

[1,0,1,0,1,0,1,0,1,1,0,0] => 8

[1,0,1,0,1,0,1,1,0,0,1,0] => 8

[1,0,1,0,1,0,1,1,0,1,0,0] => 4

[1,0,1,0,1,0,1,1,1,0,0,0] => 8

[1,0,1,0,1,1,0,0,1,0,1,0] => 8

[1,0,1,0,1,1,0,0,1,1,0,0] => 8

[1,0,1,0,1,1,0,1,0,0,1,0] => 2

[1,0,1,0,1,1,0,1,0,1,0,0] => 4

[1,0,1,0,1,1,0,1,1,0,0,0] => 2

[1,0,1,0,1,1,1,0,0,0,1,0] => 8

[1,0,1,0,1,1,1,0,0,1,0,0] => 4

[1,0,1,0,1,1,1,0,1,0,0,0] => 2

[1,0,1,0,1,1,1,1,0,0,0,0] => 8

[1,0,1,1,0,0,1,0,1,0,1,0] => 8

[1,0,1,1,0,0,1,0,1,1,0,0] => 8

[1,0,1,1,0,0,1,1,0,0,1,0] => 8

[1,0,1,1,0,0,1,1,0,1,0,0] => 4

[1,0,1,1,0,0,1,1,1,0,0,0] => 8

[1,0,1,1,0,1,0,0,1,0,1,0] => 2

[1,0,1,1,0,1,0,0,1,1,0,0] => 2

[1,0,1,1,0,1,0,1,0,0,1,0] => 4

[1,0,1,1,0,1,0,1,0,1,0,0] => 2

[1,0,1,1,0,1,0,1,1,0,0,0] => 4

[1,0,1,1,0,1,1,0,0,0,1,0] => 2

[1,0,1,1,0,1,1,0,0,1,0,0] => -4

[1,0,1,1,0,1,1,0,1,0,0,0] => 2

[1,0,1,1,0,1,1,1,0,0,0,0] => 2

[1,0,1,1,1,0,0,0,1,0,1,0] => 8

[1,0,1,1,1,0,0,0,1,1,0,0] => 8

[1,0,1,1,1,0,0,1,0,0,1,0] => 2

[1,0,1,1,1,0,0,1,0,1,0,0] => 4

[1,0,1,1,1,0,0,1,1,0,0,0] => 2

[1,0,1,1,1,0,1,0,0,0,1,0] => 0

[1,0,1,1,1,0,1,0,0,1,0,0] => 2

[1,0,1,1,1,0,1,0,1,0,0,0] => 2

[1,0,1,1,1,0,1,1,0,0,0,0] => 0

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Description

The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra.

References

[1] de la Peña, José A. Algebras whose Coxeter polynomials are products of cyclotomic polynomials MathSciNet:3254775 DOI:10.1007/s10468-013-9424-0

Code

z:=7;R:=BuildSequencesLNak(z);temp:=[];for i in R do Append(temp,[[i,Value(CoxeterPolynomial(NakayamaAlgebra(i,GF(3))),1)]]);od;temp;

Created

Sep 03, 2017 at 14:16 by Rene Marczinzik

Updated

Sep 03, 2017 at 14:49 by Martin Rubey