N=3 k=1: dim Fix_O_N=0 (pairings 0); dim Fix^xi=1 (NC_2,1: 1); dim(sum)=1; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.2s]
N=3 k=2: dim Fix_O_N=1 (pairings 1); dim Fix^xi=2 (NC_2,1: 2); dim(sum)=2; dim intersection=1; Catalan=1; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.0s]
N=3 k=3: dim Fix_O_N=0 (pairings 0); dim Fix^xi=4 (NC_2,1: 4); dim(sum)=4; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 4, rank 4, independent: True  [0.0s]
N=3 k=4: dim Fix_O_N=3 (pairings 3); dim Fix^xi=9 (NC_2,1: 9); dim(sum)=10; dim intersection=2; Catalan=2; equal: True | Prop 4.6(3) vectors: 7, rank 7, independent: True  [0.0s]
N=3 k=5: dim Fix_O_N=0 (pairings 0); dim Fix^xi=21 (NC_2,1: 21); dim(sum)=21; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 21, rank 21, independent: True  [0.0s]
N=3 k=6: dim Fix_O_N=15 (pairings 15); dim Fix^xi=51 (NC_2,1: 51); dim(sum)=61; dim intersection=5; Catalan=5; equal: True | Prop 4.6(3) vectors: 46, rank 46, independent: True  [0.0s]
N=3 k=7: dim Fix_O_N=0 (pairings 0); dim Fix^xi=127 (NC_2,1: 127); dim(sum)=127; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 127, rank 127, independent: True  [0.4s]
N=3 k=8: dim Fix_O_N=91 (pairings 105); dim Fix^xi=323 (NC_2,1: 323); dim(sum)=400; dim intersection=14; Catalan=14; equal: True | Prop 4.6(3) vectors: 309, rank 309, independent: True  [47.9s]
N=4 k=1: dim Fix_O_N=0 (pairings 0); dim Fix^xi=1 (NC_2,1: 1); dim(sum)=1; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.1s]
N=4 k=2: dim Fix_O_N=1 (pairings 1); dim Fix^xi=2 (NC_2,1: 2); dim(sum)=2; dim intersection=1; Catalan=1; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.0s]
N=4 k=3: dim Fix_O_N=0 (pairings 0); dim Fix^xi=4 (NC_2,1: 4); dim(sum)=4; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 4, rank 4, independent: True  [0.0s]
N=4 k=4: dim Fix_O_N=3 (pairings 3); dim Fix^xi=9 (NC_2,1: 9); dim(sum)=10; dim intersection=2; Catalan=2; equal: True | Prop 4.6(3) vectors: 7, rank 7, independent: True  [0.0s]
N=4 k=5: dim Fix_O_N=0 (pairings 0); dim Fix^xi=21 (NC_2,1: 21); dim(sum)=21; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 21, rank 21, independent: True  [0.0s]
N=4 k=6: dim Fix_O_N=15 (pairings 15); dim Fix^xi=51 (NC_2,1: 51); dim(sum)=61; dim intersection=5; Catalan=5; equal: True | Prop 4.6(3) vectors: 46, rank 46, independent: True  [0.0s]
N=4 k=7: dim Fix_O_N=0 (pairings 0); dim Fix^xi=127 (NC_2,1: 127); dim(sum)=127; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 127, rank 127, independent: True  [0.5s]
N=4 k=8: dim Fix_O_N=105 (pairings 105); dim Fix^xi=323 (NC_2,1: 323); dim(sum)=414; dim intersection=14; Catalan=14; equal: True | Prop 4.6(3) vectors: 309, rank 309, independent: True  [112.1s]
N=5 k=1: dim Fix_O_N=0 (pairings 0); dim Fix^xi=1 (NC_2,1: 1); dim(sum)=1; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.1s]
N=5 k=2: dim Fix_O_N=1 (pairings 1); dim Fix^xi=2 (NC_2,1: 2); dim(sum)=2; dim intersection=1; Catalan=1; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.0s]
N=5 k=3: dim Fix_O_N=0 (pairings 0); dim Fix^xi=4 (NC_2,1: 4); dim(sum)=4; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 4, rank 4, independent: True  [0.0s]
N=5 k=4: dim Fix_O_N=3 (pairings 3); dim Fix^xi=9 (NC_2,1: 9); dim(sum)=10; dim intersection=2; Catalan=2; equal: True | Prop 4.6(3) vectors: 7, rank 7, independent: True  [0.0s]
N=5 k=5: dim Fix_O_N=0 (pairings 0); dim Fix^xi=21 (NC_2,1: 21); dim(sum)=21; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 21, rank 21, independent: True  [0.0s]
N=5 k=6: dim Fix_O_N=15 (pairings 15); dim Fix^xi=51 (NC_2,1: 51); dim(sum)=61; dim intersection=5; Catalan=5; equal: True | Prop 4.6(3) vectors: 46, rank 46, independent: True  [0.0s]
N=5 k=7: dim Fix_O_N=0 (pairings 0); dim Fix^xi=127 (NC_2,1: 127); dim(sum)=127; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 127, rank 127, independent: True  [0.7s]
N=5 k=8: dim Fix_O_N=105 (pairings 105); dim Fix^xi=323 (NC_2,1: 323); dim(sum)=414; dim intersection=14; Catalan=14; equal: True | Prop 4.6(3) vectors: 309, rank 309, independent: True  [167.3s]
N=6 k=1: dim Fix_O_N=0 (pairings 0); dim Fix^xi=1 (NC_2,1: 1); dim(sum)=1; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.1s]
N=6 k=2: dim Fix_O_N=1 (pairings 1); dim Fix^xi=2 (NC_2,1: 2); dim(sum)=2; dim intersection=1; Catalan=1; equal: True | Prop 4.6(3) vectors: 1, rank 1, independent: True  [0.0s]
N=6 k=3: dim Fix_O_N=0 (pairings 0); dim Fix^xi=4 (NC_2,1: 4); dim(sum)=4; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 4, rank 4, independent: True  [0.0s]
N=6 k=4: dim Fix_O_N=3 (pairings 3); dim Fix^xi=9 (NC_2,1: 9); dim(sum)=10; dim intersection=2; Catalan=2; equal: True | Prop 4.6(3) vectors: 7, rank 7, independent: True  [0.0s]
N=6 k=5: dim Fix_O_N=0 (pairings 0); dim Fix^xi=21 (NC_2,1: 21); dim(sum)=21; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 21, rank 21, independent: True  [0.0s]
N=6 k=6: dim Fix_O_N=15 (pairings 15); dim Fix^xi=51 (NC_2,1: 51); dim(sum)=61; dim intersection=5; Catalan=5; equal: True | Prop 4.6(3) vectors: 46, rank 46, independent: True  [0.0s]
N=6 k=7: dim Fix_O_N=0 (pairings 0); dim Fix^xi=127 (NC_2,1: 127); dim(sum)=127; dim intersection=0; Catalan=0; equal: True | Prop 4.6(3) vectors: 127, rank 127, independent: True  [0.8s]
N=6 k=8: dim Fix_O_N=105 (pairings 105); dim Fix^xi=323 (NC_2,1: 323); dim(sum)=414; dim intersection=14; Catalan=14; equal: True | Prop 4.6(3) vectors: 309, rank 309, independent: True  [217.9s]
