# r2_slice.py: Lemma 4.9 (Y_s = R_s), Lemma 4.5, Lemma 4.6(c) for all sign vectors of length <= 10
m= 0: sign vectors     1, Y_s = R_s exactly for     1, mismatches 0; sign vectors with NC(s) non-empty    1; max dim Y_s = 1, sum of dim Y_s = 1; Lemma 4.6(c): 1 pairs (s,t), disagreements 0; Lemma 4.5: 1 of 1 noncrossing pairings give dimension 1   [0.0s]
m= 1: sign vectors     2, Y_s = R_s exactly for     2, mismatches 0; sign vectors with NC(s) non-empty    0; max dim Y_s = 0, sum of dim Y_s = 0; Lemma 4.6(c): 4 pairs (s,t), disagreements 0; Lemma 4.5: 0 of 0 noncrossing pairings give dimension 1   [0.0s]
m= 2: sign vectors     4, Y_s = R_s exactly for     4, mismatches 0; sign vectors with NC(s) non-empty    2; max dim Y_s = 1, sum of dim Y_s = 2; Lemma 4.6(c): 16 pairs (s,t), disagreements 0; Lemma 4.5: 1 of 1 noncrossing pairings give dimension 1   [0.0s]
m= 3: sign vectors     8, Y_s = R_s exactly for     8, mismatches 0; sign vectors with NC(s) non-empty    0; max dim Y_s = 0, sum of dim Y_s = 0; Lemma 4.6(c): 64 pairs (s,t), disagreements 0; Lemma 4.5: 0 of 0 noncrossing pairings give dimension 1   [0.0s]
m= 4: sign vectors    16, Y_s = R_s exactly for    16, mismatches 0; sign vectors with NC(s) non-empty    6; max dim Y_s = 2, sum of dim Y_s = 8; Lemma 4.6(c): 256 pairs (s,t), disagreements 0; Lemma 4.5: 2 of 2 noncrossing pairings give dimension 1   [0.0s]
m= 5: sign vectors    32, Y_s = R_s exactly for    32, mismatches 0; sign vectors with NC(s) non-empty    0; max dim Y_s = 0, sum of dim Y_s = 0; Lemma 4.6(c): 1024 pairs (s,t), disagreements 0; Lemma 4.5: 0 of 0 noncrossing pairings give dimension 1   [0.0s]
m= 6: sign vectors    64, Y_s = R_s exactly for    64, mismatches 0; sign vectors with NC(s) non-empty   20; max dim Y_s = 5, sum of dim Y_s = 40; Lemma 4.6(c): 4096 pairs (s,t), disagreements 0; Lemma 4.5: 5 of 5 noncrossing pairings give dimension 1   [0.0s]
m= 7: sign vectors   128, Y_s = R_s exactly for   128, mismatches 0; sign vectors with NC(s) non-empty    0; max dim Y_s = 0, sum of dim Y_s = 0; Lemma 4.6(c): 16384 pairs (s,t), disagreements 0; Lemma 4.5: 0 of 0 noncrossing pairings give dimension 1   [0.0s]
m= 8: sign vectors   256, Y_s = R_s exactly for   256, mismatches 0; sign vectors with NC(s) non-empty   70; max dim Y_s = 14, sum of dim Y_s = 224; Lemma 4.6(c): 65536 pairs (s,t), disagreements 0; Lemma 4.5: 14 of 14 noncrossing pairings give dimension 1   [0.3s]
m= 9: sign vectors   512, Y_s = R_s exactly for   512, mismatches 0; sign vectors with NC(s) non-empty    0; max dim Y_s = 0, sum of dim Y_s = 0; Lemma 4.6(c): 262144 pairs (s,t), disagreements 0; Lemma 4.5: 0 of 0 noncrossing pairings give dimension 1   [1.0s]
m=10: sign vectors  1024, Y_s = R_s exactly for  1024, mismatches 0; sign vectors with NC(s) non-empty  252; max dim Y_s = 42, sum of dim Y_s = 1344; Lemma 4.6(c): 1048576 pairs (s,t), disagreements 0; Lemma 4.5: 42 of 42 noncrossing pairings give dimension 1   [4.7s]
total number of sign vectors examined: 2047
