/// <summary>
///
/// </summary>
/// <param name="numRows">The number of rows of vertices.</param>
/// <param name="firstVertex"></param>
/// <returns></returns>
public static Quiver <int> GetSquareQuiver(int numRows, int firstVertex = DefaultFirstVertex)
{
if (!SquareParameterIsValid(numRows))
{
throw new ArgumentOutOfRangeException(nameof(numRows));
}
if (numRows == 1)
{
return(new Quiver <int>(vertices: new int[] { firstVertex }, arrows: new Arrow <int> [0]));
}
// Sort of backwards to construct the entire QP only to return just the quiver
// But this reduces duplicated logic
var qp = UsefulQPs.GetSquareQP(numRows, firstVertex);
return(qp.Quiver);
}
public SelfInjectiveQP <int> GetSelfInjectiveSquareQP(int numRows, int firstVertex = DefaultFirstVertex)
{
if (!SquareParameterIsValid(numRows))
{
throw new ArgumentOutOfRangeException(nameof(numRows));
}
var qp = UsefulQPs.GetSquareQP(numRows);
int numVerticesInRow = numRows;
int numVertices = numRows * numVerticesInRow;
// Rotation "twice" clockwise/counterclockwise to get the Nakayama permutation
// This map happens to be just "x mapsto (n+1)-x" (labeling the vertices from 0 would be cleaner here I guess)
var nakayamaPermutation = Enumerable.Range(1, numVertices).ToDictionary(x => x, x => numVertices + 1 - x);
return(new SelfInjectiveQP <int>(qp, nakayamaPermutation));
}
