R_3: sigma(x,y) = (y, 2y-x): {'ybe': True, 'bijective': True, 'left_nondeg': True, 'right_nondeg': True, 'involutive': False, 'idempotent': False}
square-free (sigma(x,x) = (x,x)): True ; sigma^2 != id: True
sigma-orbits on X x X: [[(0, 0)], [(0, 1), (1, 2), (2, 0)], [(0, 2), (2, 1), (1, 0)], [(1, 1)], [(2, 2)]]
dim A_n (monoid classes), n=0..8: [1, 3, 5, 6, 6, 6, 6, 6, 6] ; Walton-Zhang Thm 3.10(1) series: [1, 3, 5, 6, 6, 6, 6, 6, 6] ; equal: True
dim B_n (exact), n=0..6: [1, 3, 4, 3, 1, 0, 0] ; QS_6 is the zero matrix: True
dim E_n = dim (T(V)/(orbit sums))_n, n=0..6: [1, 3, 4, 3, 1, 0, 0]
dim K_n (exact), n=0..6: [1, 3, 4, 3, 1, 0, 0]
dim ker(1-sigma) = 5 = number of orbits 5 ; orbit sums in the kernel: True
FK_3 relations (WZ Def 0.1, a=x12, b=x23, c=-x13) span the orbit sums: ranks 5, 5, union 5: True
H_A(t) H_B(-t) up to t^8: [1, 0, 0, 0, 0, 0, -1, 0, 0]
weight 1: dims C_0..C_1 = [6, 3], dim A_w = 3; H_-1=0, H_n = [0, 0]
weight 2: dims C_0..C_2 = [19, 18, 4], dim A_w = 5; H_-1=0, H_n = [0, 0, 0]
weight 3: dims C_0..C_3 = [42, 57, 24, 3], dim A_w = 6; H_-1=0, H_n = [0, 0, 0, 0]
weight 4: dims C_0..C_4 = [73, 126, 76, 18, 1], dim A_w = 6; H_-1=0, H_n = [0, 0, 0, 0, 0]
weight 5: dims C_0..C_5 = [108, 219, 168, 57, 6, 0], dim A_w = 6; H_-1=0, H_n = [0, 0, 0, 0, 0, 0]
weight 6: dims C_0..C_6 = [144, 324, 292, 126, 19, 0, 0], dim A_w = 6; H_-1=0, H_n = [0, 0, 0, 1, 0, 0, 0]
time 1.6s
