N=4 m=7: Fix_SO_N = 0; intersection 0; Catalan=0
N=4 m=8: spanning vectors=315 (Brauer 105, det-type 210); dim Fix_SO_N=196 (mod p 196); rank on non-trivial words=182 (mod p 182); dim intersection=14 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=14; equal: True  [6.7s]
N=5 m=8: spanning vectors=105 (Brauer 105, det-type 0); dim Fix_SO_N=105 (mod p 105); rank on non-trivial words=91 (mod p 91); dim intersection=14 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=14; equal: True  [0.8s]
N=6 m=2: spanning vectors=1 (Brauer 1, det-type 0); dim Fix_SO_N=1 (mod p 1); rank on non-trivial words=0 (mod p 0); dim intersection=1 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=1; equal: True  [0.1s]
N=6 m=3: Fix_SO_N = 0; intersection 0; Catalan=0
N=6 m=4: spanning vectors=3 (Brauer 3, det-type 0); dim Fix_SO_N=3 (mod p 3); rank on non-trivial words=1 (mod p 1); dim intersection=2 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=2; equal: True  [0.0s]
N=6 m=5: Fix_SO_N = 0; intersection 0; Catalan=0
N=6 m=6: spanning vectors=16 (Brauer 15, det-type 1); dim Fix_SO_N=16 (mod p 16); rank on non-trivial words=11 (mod p 11); dim intersection=5 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=5; equal: True  [0.0s]
N=6 m=7: Fix_SO_N = 0; intersection 0; Catalan=0
N=6 m=8: spanning vectors=133 (Brauer 105, det-type 28); dim Fix_SO_N=126 (mod p 126); rank on non-trivial words=112 (mod p 112); dim intersection=14 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=14; equal: True  [1.0s]
N=7 m=2: spanning vectors=1 (Brauer 1, det-type 0); dim Fix_SO_N=1 (mod p 1); rank on non-trivial words=0 (mod p 0); dim intersection=1 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=1; equal: True  [0.1s]
N=7 m=4: spanning vectors=3 (Brauer 3, det-type 0); dim Fix_SO_N=3 (mod p 3); rank on non-trivial words=1 (mod p 1); dim intersection=2 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=2; equal: True  [0.0s]
N=7 m=6: spanning vectors=15 (Brauer 15, det-type 0); dim Fix_SO_N=15 (mod p 15); rank on non-trivial words=10 (mod p 10); dim intersection=5 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=5; equal: True  [0.0s]
N=7 m=7: spanning vectors=1 (Brauer 0, det-type 1); dim Fix_SO_N=1 (mod p 1); rank on non-trivial words=1 (mod p 1); dim intersection=0 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=0; equal: True  [0.0s]
N=7 m=8: spanning vectors=105 (Brauer 105, det-type 0); dim Fix_SO_N=105 (mod p 105); rank on non-trivial words=91 (mod p 91); dim intersection=14 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=14; equal: True  [1.0s]
