public static Quiver <int> GetCycleQuiver(int numVertices, int firstVertex = DefaultFirstVertex)
{
if (!CycleParameterIsValid(numVertices))
{
throw new ArgumentOutOfRangeException(nameof(numVertices));
}
// Sort of backwards to construct the entire QP only to return just the quiver
// But this reduces duplicated logic
var qp = UsefulQPs.GetCycleQP(numVertices, firstVertex);
return(qp.Quiver);
}
public SelfInjectiveQP <int> GetSelfInjectiveCycleQP(int numVertices, int firstVertex = DefaultFirstVertex)
{
if (numVertices < 3)
{
throw new ArgumentOutOfRangeException(nameof(numVertices));
}
var qp = UsefulQPs.GetCycleQP(numVertices, firstVertex);
int n = numVertices;
var dict = Enumerable.Range(firstVertex, n).ToDictionary(k => k, k => (k - 2 - firstVertex).Modulo(n) + firstVertex);
var nakayamaPermutation = new NakayamaPermutation <int>(dict);
var selfInjectiveQp = new SelfInjectiveQP <int>(qp, nakayamaPermutation);
return(selfInjectiveQp);
}
