public static Quiver <int> GetOddFlowerQuiver(int numVerticesInCenterPolygon, int firstVertex = DefaultFirstVertex)
{
if (!OddFlowerParameterIsValid(numVerticesInCenterPolygon))
{
throw new ArgumentOutOfRangeException(nameof(numVerticesInCenterPolygon));
}
// Sort of backwards to construct the entire QP only to return just the quiver
// But this reduces duplicated logic
var qp = UsefulQPs.GetOddFlowerQP(numVerticesInCenterPolygon, firstVertex);
return(qp.Quiver);
}
/// <remarks>It is <em>assumed</em> that <em>all</em> odd flower QPs are self-injective.</remarks>
public SelfInjectiveQP <int> GetSelfInjectiveOddFlowerQP(int numVerticesInCenterPolygon, int firstVertex = DefaultFirstVertex)
{
if (numVerticesInCenterPolygon < 3 || numVerticesInCenterPolygon.Modulo(2) == 0)
{
throw new ArgumentOutOfRangeException(nameof(numVerticesInCenterPolygon));
}
var qp = UsefulQPs.GetOddFlowerQP(numVerticesInCenterPolygon);
int numLayers = (numVerticesInCenterPolygon + 1) / 2;
int numVerticesInFullInnerLayer = 2 * numVerticesInCenterPolygon;
int numVerticesInOuterLayer = 2 * numVerticesInFullInnerLayer;
// Rotate clockwise by 2*pi / ((numVerticesInCenterPolygon-1)/2) for the Nakayama permutation?
var nakayamaPermutation = new Dictionary <int, int>();
for (int layerIndex = 0; layerIndex < numLayers; layerIndex++)
{
var layer = GetLayerVertices(layerIndex);
for (int indexInLayer = 0; indexInLayer < layer.Count; indexInLayer++)
{
int input = layer[indexInLayer];
int stepsToRotateBy = (numVerticesInCenterPolygon - 1) / 2 * (layer.Count / numVerticesInCenterPolygon);
int output = layer[indexInLayer + stepsToRotateBy];
nakayamaPermutation[input] = output;
}
}
return(new SelfInjectiveQP <int>(qp, nakayamaPermutation));
CircularList <int> GetLayerVertices(int layerIndex) // 0-based layer index
{
if (layerIndex == 0)
{
return(new CircularList <int>(Enumerable.Range(1, numVerticesInCenterPolygon)));
}
int startVertex = layerIndex * numVerticesInFullInnerLayer - numVerticesInCenterPolygon + 1;
int numVertices = layerIndex < numLayers - 1 ? numVerticesInFullInnerLayer : numVerticesInOuterLayer;
return(new CircularList <int>(Enumerable.Range(startVertex, numVertices)));
}
}