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def ASM_X_ray(A):
P = A.to_matrix()
n = P.nrows()
return tuple(sum(P[k-1-j][j] for j in range(max(0, k-n), min(k,n)))
for k in range(1,2*n))
@cached_function
def ASM_X_rays(n):
return sorted(ASM_X_ray(A) for A in AlternatingSignMatrices(n))
def statistic(A):
return ASM_X_rays(A.to_matrix().nrows()).count(ASM_X_ray(A))
parent_initializer = AlternatingSignMatrices
element_repr = lambda X: str([list(row) for row in X.to_matrix()])
levels = [2, 3, 4]
for level in levels:
for elt in parent_initializer(level):
print('%s => %s' % (element_repr(elt), statistic(elt)))
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