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Identifier
Values
=>
Cc0005;cc-rep
[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 [1,0,1,1,1,1,0,0,0,0,1,0]=>8 [1,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,0]=>2 [1,0,1,1,1,1,0,1,0,0,0,0]=>2 [1,0,1,1,1,1,1,0,0,0,0,0]=>8 [1,1,0,0,1,0,1,0,1,0,1,0]=>8 [1,1,0,0,1,0,1,0,1,1,0,0]=>8 [1,1,0,0,1,0,1,1,0,0,1,0]=>8 [1,1,0,0,1,0,1,1,0,1,0,0]=>4 [1,1,0,0,1,0,1,1,1,0,0,0]=>8 [1,1,0,0,1,1,0,0,1,0,1,0]=>8 [1,1,0,0,1,1,0,0,1,1,0,0]=>8 [1,1,0,0,1,1,0,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,1,0,0]=>4 [1,1,0,0,1,1,0,1,1,0,0,0]=>2 [1,1,0,0,1,1,1,0,0,0,1,0]=>8 [1,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,0,1,0,0,0]=>2 [1,1,0,0,1,1,1,1,0,0,0,0]=>8 [1,1,0,1,0,0,1,0,1,0,1,0]=>4 [1,1,0,1,0,0,1,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,0]=>0 [1,1,0,1,0,0,1,1,1,0,0,0]=>4 [1,1,0,1,0,1,0,0,1,0,1,0]=>4 [1,1,0,1,0,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,1,0,1,0,0]=>2 [1,1,0,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,0,1,1,0,0,0,1,0]=>4 [1,1,0,1,0,1,1,0,0,1,0,0]=>0 [1,1,0,1,0,1,1,0,1,0,0,0]=>2 [1,1,0,1,0,1,1,1,0,0,0,0]=>4 [1,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,1,0,0,1,0,0,1,0]=>-4 [1,1,0,1,1,0,0,1,0,1,0,0]=>0 [1,1,0,1,1,0,0,1,1,0,0,0]=>-4 [1,1,0,1,1,0,1,0,0,0,1,0]=>2 [1,1,0,1,1,0,1,0,0,1,0,0]=>2 [1,1,0,1,1,0,1,0,1,0,0,0]=>0 [1,1,0,1,1,0,1,1,0,0,0,0]=>2 [1,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,1,0,1,1,1,0,0,0,1,0,0]=>0 [1,1,0,1,1,1,0,0,1,0,0,0]=>-4 [1,1,0,1,1,1,0,1,0,0,0,0]=>2 [1,1,0,1,1,1,1,0,0,0,0,0]=>4 [1,1,1,0,0,0,1,0,1,0,1,0]=>8 [1,1,1,0,0,0,1,0,1,1,0,0]=>8 [1,1,1,0,0,0,1,1,0,0,1,0]=>8 [1,1,1,0,0,0,1,1,0,1,0,0]=>4 [1,1,1,0,0,0,1,1,1,0,0,0]=>8 [1,1,1,0,0,1,0,0,1,0,1,0]=>2 [1,1,1,0,0,1,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,1,0,0,1,0]=>4 [1,1,1,0,0,1,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,0,1,1,0,0,0]=>4 [1,1,1,0,0,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,1,0,0,1,0,0]=>-4 [1,1,1,0,0,1,1,0,1,0,0,0]=>2 [1,1,1,0,0,1,1,1,0,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,0,1,0]=>2 [1,1,1,0,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,1,0,0,1,0,0,1,0]=>2 [1,1,1,0,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,0,1,0,0,0,1,0]=>2 [1,1,1,0,1,0,1,0,0,1,0,0]=>0 [1,1,1,0,1,0,1,0,1,0,0,0]=>2 [1,1,1,0,1,0,1,1,0,0,0,0]=>2 [1,1,1,0,1,1,0,0,0,0,1,0]=>2 [1,1,1,0,1,1,0,0,0,1,0,0]=>-4 [1,1,1,0,1,1,0,0,1,0,0,0]=>0 [1,1,1,0,1,1,0,1,0,0,0,0]=>2 [1,1,1,0,1,1,1,0,0,0,0,0]=>2 [1,1,1,1,0,0,0,0,1,0,1,0]=>8 [1,1,1,1,0,0,0,0,1,1,0,0]=>8 [1,1,1,1,0,0,0,1,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,1,0,0]=>4 [1,1,1,1,0,0,0,1,1,0,0,0]=>2 [1,1,1,1,0,0,1,0,0,0,1,0]=>0 [1,1,1,1,0,0,1,0,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,1,0,0,0]=>2 [1,1,1,1,0,0,1,1,0,0,0,0]=>0 [1,1,1,1,0,1,0,0,0,0,1,0]=>2 [1,1,1,1,0,1,0,0,0,1,0,0]=>2 [1,1,1,1,0,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,1,0,0,0,0]=>2 [1,1,1,1,0,1,1,0,0,0,0,0]=>2 [1,1,1,1,1,0,0,0,0,0,1,0]=>8 [1,1,1,1,1,0,0,0,0,1,0,0]=>4 [1,1,1,1,1,0,0,0,1,0,0,0]=>2 [1,1,1,1,1,0,0,1,0,0,0,0]=>2 [1,1,1,1,1,0,1,0,0,0,0,0]=>4 [1,1,1,1,1,1,0,0,0,0,0,0]=>8
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Description
The value $p(1)$ for the Coxeter polynomial $p$ of the linear Nakayama algebra corresponding to a Dyck path.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
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
gap('LoadPackage("QPA");')

def kupisch(D):
    DR = D.reverse()
    H = DR.heights()
    return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]

def statistic(D):
    K = kupisch(D)
    A = gap.NakayamaAlgebra(K, gap.GF(3))
    p = gap.CoxeterPolynomial(A)
    return ZZ(gap.Value(p, 1))
Created
Sep 03, 2017 at 14:16 by Rene Marczinzik
Updated
Mar 11, 2026 at 18:26 by Nupur Jain