Steenrod operations in Ext

This page documents some Steenrod operations I calculated with the Ext resolver. The results are expressed in terms of the basis one finds here. These are intended to be complementary to Bruner's calculations.

For some of them, I also express the result in terms of Bruner's basis.

tmftmf

Name Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8
h0h_0h1h_1h02h_0^2
h1h_1h2h_2h12h_1^2
h2h_200h22h_2^2
c0c_000h2βh_2 \betah0e0h_0 e_000
α\alpha0000γ\gammaα2\alpha^2
β\beta000000β2\beta^2
w1w_1gg000000w12w_1^2
d0d_00000β2\beta^200d02d_0^2
e0e_0000000βg\beta ge02e_0^2
gg00000000g2g^2
γ\gamma00000000h2w2h_2 w_2γ2\gamma^2
δ\delta0000000000w2h2βw_2 h_2 \betaw2h2d0w_2 h_2 d_000
w2w_20000000000000000w22w_2^2

S2S_2

s=3s = 3

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3
c0c_0 8 [1][1] [1][1] [1,1][1, 1] [1][1] [1][1]
c1c_1 19 [1][1] [1][1] [1,1][1, 1] [1][1] [0,1][0, 1]
c2c_2 41 [1][1] [1][1] [0,1][0, 1] [1,1][1, 1] [0,1][0, 1]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3
c0c_0 8 [1][1] c1c_1 f0f_0 h0e0h_0 e_0 h12d0h_1^2 d_0
c1c_1 19 [1][1] c2c_2 f1f_1 h1e1h_1 e_1 h1xh_1 x
c2c_2 41 [1][1] c3c_3

s=4s = 4

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4
f0f_0 18 [1,1][1, 1] [1,1][1, 1] [0][0] [1,1][1, 1] [1,1][1, 1] [][]
pp' 69 [1][1] [1,0][1, 0] [0,0,1][0, 0, 1] [0,1,1,1][0, 1, 1, 1] [0,0,0,1][0, 0, 0, 1] [0,1,0][0, 1, 0]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4
f0f_0 18 [1,1][1, 1] f1f_1 00 YY h3rh_3 r 00
pp' 69 [1][1]

s=5s = 5

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5
Ph1Ph_1 9 [1][1] [1][1] [][] [][] [][] [1][1] [1][1]
Ph2Ph_2 11 [1][1] [][] [1][1] [][] [][] [1,0][1, 0] [1][1]
nn 31 [0,1][0, 1] [1,1][1, 1] [1][1] [0,1][0, 1] [1,0,1][1, 0, 1] [0,1,1][0, 1, 1] [0,0,0][0, 0, 0]
xx 37 [1][1] [1][1] [0,0,0][0, 0, 0] [1,1,1,0][1, 1, 1, 0] [0,1][0, 1] [1,1][1, 1] [1][1]
D1D_1 52 [1][1] [1][1] [0,1][0, 1] [1,1][1, 1] [1][1] [0][0] [0][0]
H1?H_1? 62 [1,0,0][1, 0, 0] [0,0,1][0, 0, 1] [0,1,1,1][0, 1, 1, 1] [0,1,0,0,1][0, 1, 0, 0, 1] [1,1,1,0,1,1][1, 1, 1, 0, 1, 1] [0,1,0,1,1][0, 1, 0, 1, 1] [1,1,1,0,0][1, 1, 1, 0, 0]
Q3?Q_3? 67 [1,0][1, 0] [1,0][1, 0] [0,1][0, 1] [0,0,1][0, 0, 1] [1,0][1, 0] [0,1][0, 1] [1][1]
n1n_1 67 [1,1][1, 1] [1,1][1, 1] [0,1][0, 1] [0,1,0][0, 1, 0] [0,1][0, 1] [1,0][1, 0] [0][0]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5
nn 31 [0,1][0, 1] n1n_1 r1r_1 h2h5n+h3D2h_2 h_5 n + h_3 D_2 h22D2+h3Q2h_2^2 D_2 + h_3 Q_2 h1x8,32+h5d0f0h_1 x_{8, 32} + h_5 d_0 f_0 00
xx 37 [1][1] x1x_1 00 1 x2x^2
D1D_1 52 [1][1] 2 3 00 00
H1?H_1? 62 [1,0,0][1, 0, 0]
Q3?Q_3? 67 [1,0][1, 0]
n1n_1 67 [1,1][1, 1]

1  This is not h02h_0^2-divisible

2  This is not h1h_1-divisible

3  This is not h0h_0-divisible

s=6s = 6

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6
rr 30 [1][1] [1][1] [0,0][0, 0] [0,0,0][0, 0, 0] [0,0,0][0, 0, 0] [1,1,0][1, 1, 0] [0,0][0, 0] [1,1][1, 1]
CC 50 [1][1] [1][1] [0][0] [1][1] [1][1] [0,0,1][0, 0, 1] [1,0,0][1, 0, 0] [0,0,0][0, 0, 0]
GG 54 [1][1] [1][1] [1,0][1, 0] [0,1,1][0, 1, 1] [0,0,1,0][0, 0, 1, 0] [1,0,0][1, 0, 0] [][] [][]
D2D_2 58 [1][1] [][] [1,0][1, 0] [1][1] [0][0] [0,1,0][0, 1, 0] [0,1,1][0, 1, 1] [0,1][0, 1]
A?A? 61 [1,0][1, 0] [0,1,0,0][0, 1, 0, 0] [0,1,1,0,0][0, 1, 1, 0, 0] [1,0,0,1,0,0][1, 0, 0, 1, 0, 0] [1,1,0,0,0][1, 1, 0, 0, 0] [0,1,0,1,1][0, 1, 0, 1, 1] [0,0,0,1,1][0, 0, 0, 1, 1] [1,0,1][1, 0, 1]
A?A'? 61 [0,1][0, 1] [1,0,1,0][1, 0, 1, 0] [0,1,0,1,1][0, 1, 0, 1, 1] [1,0,0,0,0,1][1, 0, 0, 0, 0, 1] [1,1,1,1,0][1, 1, 1, 1, 0] [0,0,0,1,0][0, 0, 0, 1, 0] [0,0,1,1,0][0, 0, 1, 1, 0] [1,1,1][1, 1, 1]
AA'' 64 [1][1] [1][1] [0,1,0][0, 1, 0] [1,1,1,1,0][1, 1, 1, 1, 0] [0,1,0,1,0][0, 1, 0, 1, 0] [0,0,0,0,0][0, 0, 0, 0, 0] [0,0,1,0,1,1][0, 0, 1, 0, 1, 1] [0,0,0,0,0][0, 0, 0, 0, 0]
r1r_1 66 [1][1] [0,1][0, 1] [0,0,0][0, 0, 0] [0,0][0, 0] [0,0][0, 0] [1][1] [0,0,0][0, 0, 0] [0,0,0,0,0][0, 0, 0, 0, 0]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6
rr 30 [1][1] r1r_1 00 00 00 h1X1+x10,27+x10,28h_1 X_1 + x_{10, 27} + x_{10, 28} 4 00 r2r^2
CC 50 [1][1] 00 h1h3x8,80h_1 h_3 x_{8, 80} h03x8,93h_0^3 x_{8, 93} 00
GG 54 [1][1] 00 00
r1r_1 66 [1][1] r2r_2 00 00 00 00 00

4  We identify x10,27x_{10, 27} and x10,28x_{10, 28} uniquely as follows — x10,28x_{10, 28} is the unique non-zero element whose h0h_0 and h1h_1 products are both divisible by h2h_2, and x10,27+x10,28x_{10, 27} + x_{10, 28} has zero h2h_2 multiplication

s=7s = 7

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7
Pc0Pc_0 16 [1][1] [1][1] [1][1] [1][1] [][] [][] [1][1] [1][1] [1][1]
jj 26 [1][1] [][] [0][0] [1,1][1, 1] [0,0][0, 0] [1][1] [1,1][1, 1] [1,1][1, 1] [1][1]
kk 29 [1][1] [1,0][1, 0] [0,0,0][0, 0, 0] [0,1,1][0, 1, 1] [0,0,0][0, 0, 0] [1,1][1, 1] [1,1][1, 1] [0][0] [1][1]
ll 32 [1][1] [1][1] [1][1] [1,1][1, 1] [1,1][1, 1] [1,0][1, 0] [0,0][0, 0] [0,1][0, 1] [1,1][1, 1]
mm 35 [1][1] [1,0,0,1][1, 0, 0, 1] [0,0][0, 0] [1,1][1, 1] [1][1] [][] [0][0] [1,0,1][1, 0, 1] [1,1,1][1, 1, 1]
B1B_1 46 [1][1] [1,0,0][1, 0, 0] [0,1][0, 1] [1,1][1, 1] [1][1] [0,1][0, 1] [1,1][1, 1] [0,1,0,0][0, 1, 0, 0] [1,0,0][1, 0, 0]
B2?B_2? 48 [0,1][0, 1] [1,0][1, 0] [0,1,1][0, 1, 1] [0,0,1,1][0, 0, 1, 1] [1,1,1][1, 1, 1] [1][1] [1,1][1, 1] [0,1,0][0, 1, 0] [1,0][1, 0]
Q2Q_2 57 [1][1] [1,0][1, 0] [0][0] [1][1] [1,0,0][1, 0, 0] [0,1,1][0, 1, 1] [0,0][0, 0] [1,0][1, 0] [0,0,1][0, 0, 1]
B3B_3 60 [1][1] [0,0,1,0,0][0, 0, 1, 0, 0] [0,0,0,0,0,0][0, 0, 0, 0, 0, 0] [1,0,1,0,0][1, 0, 1, 0, 0] [1,0,0,0,0][1, 0, 0, 0, 0] [1,0,0,0,0][1, 0, 0, 0, 0] [1,1,0][1, 1, 0] [0][0] [0,0][0, 0]
?? 63 [0,1,0][0, 1, 0] [0,0,1][0, 0, 1] [1,0,1,1,1][1, 0, 1, 1, 1] [0,1,1,1,1][0, 1, 1, 1, 1] [0,0,0,0,1][0, 0, 0, 0, 1] [0,1,1,0,0,1][0, 1, 1, 0, 0, 1] [1,0,0,0,0][1, 0, 0, 0, 0] [0,0,1,0,0][0, 0, 1, 0, 0] [0,0,0,0][0, 0, 0, 0]
?? 63 [0,0,1][0, 0, 1] [0,1,1][0, 1, 1] [1,1,1,1,1][1, 1, 1, 1, 1] [1,0,0,1,1][1, 0, 0, 1, 1] [1,0,0,0,0][1, 0, 0, 0, 0] [0,0,0,1,1,1][0, 0, 0, 1, 1, 1] [0,0,0,0,0][0, 0, 0, 0, 0] [0,1,0,0,0][0, 1, 0, 0, 0] [0,0,0,0][0, 0, 0, 0]
?? 66 [0,1][0, 1] [0,1,1,0][0, 1, 1, 0] [1,0,1][1, 0, 1] [1,1][1, 1] [0,1,1,0,1][0, 1, 1, 0, 1] [1,0,1,0,1,1][1, 0, 1, 0, 1, 1] [1,0,1,0,0][1, 0, 1, 0, 0] [1,0,1,1,0][1, 0, 1, 1, 0] [0,0,0,1,0][0, 0, 0, 1, 0]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7
Pc0Pc_0 16 [1][1] h12P2d0h_1^2 P^2 d_0 h0P2eh_0 P^2 e h0x11,7h_0 x_{11, 7} 00 00 h2d0gh_2 d_0 g h02Yh_0^2 Y h1Yh_1 Y
jj 26 [1][1] 00 00 h02Q2h_0^2 Q_2 00 j2j^2
kk 29 [1][1] 00 h1x8,32+h5d0f0h_1 x_{8, 32} + h_5 d_0 f_0 00 00 k2k^2
ll 32 [1][1] h1G21h_1 G_{21} h3X1h_3 X_1 h02x9,40h_0^2 x_{9, 40} 00 gwgw l2l^2
mm 35 [1][1] m1m_1 00 h3G21h_3 G_{21} 00 00 m2m^2

s=8s = 8

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8
Pd0Pd_0 22 [1][1] [1][1] [0][0] [1][1] [0][0] [1][1] [0,0][0, 0] [1][1] [0][0] [1][1]
Pe0Pe_0 25 [1][1] [0][0] [0,0][0, 0] [1,1][1, 1] [1][1] [0,1][0, 1] [0,1][0, 1] [0][0] [1][1] [1][1]
?? 46 [1][1] [0,1,0,0][0, 1, 0, 0] [1,0][1, 0] [0,0][0, 0] [0,0][0, 0] [1,1][1, 1] [1][1] [0][0] [0,0][0, 0] [0][0]
?? 62 [0,1,0][0, 1, 0] [1,1,1,0,1][1, 1, 1, 0, 1] [0,0,0,1,0][0, 0, 0, 1, 0] [1,0,0,1,0][1, 0, 0, 1, 0] [0,0,0,1,1,1][0, 0, 0, 1, 1, 1] [1,1,0,1,1][1, 1, 0, 1, 1] [1,1,1,1,1][1, 1, 1, 1, 1] [0,1,1,1][0, 1, 1, 1] [0,0,0,0,1][0, 0, 0, 0, 1] [1,0,1,0,0][1, 0, 1, 0, 0]
?? 62 [0,0,1][0, 0, 1] [0,0,0,1,0][0, 0, 0, 1, 0] [0,0,0,1,0][0, 0, 0, 1, 0] [0,0,0,0,0][0, 0, 0, 0, 0] [0,0,0,0,0,0][0, 0, 0, 0, 0, 0] [0,1,0,0,1][0, 1, 0, 0, 1] [0,1,0,1,0][0, 1, 0, 1, 0] [0,0,0,1][0, 0, 0, 1] [0,1,0,0,1][0, 1, 0, 0, 1] [1,0,1,0,0][1, 0, 1, 0, 0]

s=9s = 9

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9
P2h1P^2h_1 17 [1][1] [][] [][] [0][0] [0][0] [0][0] [][] [][] [][] [1][1] [1][1]
P2h2P^2h_2 19 [1][1] [][] [][] [][] [][] [0][0] [0][0] [][] [][] [1,0][1, 0] [1][1]
uu 39 [1][1] [1][1] [0,0][0, 0] [1,0][1, 0] [][] [1][1] [0,0][0, 0] [1,1][1, 1] [0,1][0, 1] [1,0,0][1, 0, 0] [1,0,1][1, 0, 1]
vv 42 [1][1] [0][0] [0,0][0, 0] [0,0][0, 0] [0][0] [1][1] [1,0][1, 0] [1,0][1, 0] [0,1,0][0, 1, 0] [0,0,1][0, 0, 1] [0,1,0][0, 1, 0]
ww 45 [1][1] [1,0][1, 0] [0,0][0, 0] [1,0][1, 0] [0,0][0, 0] [1][1] [0][0] [1,1][1, 1] [0][0] [1,0,1][1, 0, 1] [0,1,1][0, 1, 1]
?? 60 [0,1][0, 1] [1,0,0,1][1, 0, 0, 1] [0,0,0,1][0, 0, 0, 1] [0,1,0,0][0, 1, 0, 0] [1,0,1,0,0][1, 0, 1, 0, 0] [0,0,1,0,1][0, 0, 1, 0, 1] [0,1,0,1,1][0, 1, 0, 1, 1] [0,0,1][0, 0, 1] [0,0,1][0, 0, 1] [0,0,0,1][0, 0, 0, 1] [0,0,1][0, 0, 1]
?? 61 [1][1] [1,0,1,1,0][1, 0, 1, 1, 0] [1,0,0,0,1][1, 0, 0, 0, 1] [0,1,0,1,0,1][0, 1, 0, 1, 0, 1] [1,0,0,0,0][1, 0, 0, 0, 0] [0,0,1,1,0][0, 0, 1, 1, 0] [0,0,0,0][0, 0, 0, 0] [1,1,1,0,1][1, 1, 1, 0, 1] [1,0,0,1,1][1, 0, 0, 1, 1] [1,1,1,0][1, 1, 1, 0] [0,0,1][0, 0, 1]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9
uu 39 [1][1] 00 00 00 u2u^2

s=10s = 10

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10}
zz 41 [1][1] [0,0][0, 0] [0,0][0, 0] [0][0] [0][0] [1,0][1, 0] [0,0][0, 0] [1,0,1][1, 0, 1] [0,0,1][0, 0, 1] [0,1,0][0, 1, 0] [1,1][1, 1] [1][1]
?? 53 [1][1] [][] [0][0] [0,1][0, 1] [0,0][0, 0] [1,0][1, 0] [1,0,1,0][1, 0, 1, 0] [0,1,0,0][0, 1, 0, 0] [1,0][1, 0] [0][0] [1,0,1][1, 0, 1] [0,1,0][0, 1, 0]
?? 54 [1,0][1, 0]
Q1?Q_1? 56 [0,1][0, 1]
?? 59 [1][1]
?? 62 [0,1,0][0, 1, 0]
?? 62 [0,0,1][0, 0, 1]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10}
zz 41 [1][1] 00 00 00 00 h02x12,51h_0^2 x_{12, 51} 00 g2Ng^2 N h0d2rh_0 d^2 r z2z^2

s=11s = 11

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11}
P2c0P^2 c_0 24 [1][1] [0][0] [][] [][] [][] [][] [0][0] [0][0] [][] [][] [1][1] [1][1] [1][1]
?? 34 [1][1] [0][0] [0][0] [0,0][0, 0] [0,0][0, 0] [1][1] [1][1] [1,1][1, 1] [1,0][1, 0] [1][1] [0,1][0, 1] [1,1][1, 1] [1][1]

s=12s = 12

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12}
P2d0P^2 d_0 30 [1][1] [1][1] [0,0,0][0, 0, 0] [1,1,1][1, 1, 1] [0][0] [1][1] [0][0] [0][0] [0][0] [0][0] [0,0][0, 0] [1][1] [0][0] [1][1]
P2e0P^2 e_0 33 [1][1] [0][0] [0,0][0, 0] [1,0][1, 0] [1][1] [1][1] [0,0][0, 0] [0,0][0, 0] [0][0] [0,0][0, 0] [0,1][0, 1] [0][0] [1][1] [1][1]

Name

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12}
P2d0P^2 d_0 30 [1][1] 00 00 00 00 00 00 00 00
P2e0P^2 e_0 33 [1][1] 00 00 00 00 00 00 00

s=13s = 13

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12} Sq13Sq^{13}
P3h1P^3 h_1 25 [1][1] [0][0] [0][0] [][] [][] [][] [][] [0][0] [0][0] [1][1] [][] [][] [][] [1][1] [1][1]
P3h2P^3 h_2 2727 [1][1] [][] [][] [0][0] [0][0] [0][0] [0][0] [][] [][] [0][0] [1][1] [][] [][] [1,0][1, 0] [1][1]
?? 47 [1,0][1, 0]
?? 47 [0,1][0, 1] [0][0] [0,0][0, 0] [0,0][0, 0] [0][0] [][] [0,0][0, 0] [0,0,0][0, 0, 0] [0,0][0, 0] [0,0][0, 0] [0,0][0, 0] [0,0][0, 0] [0,0][0, 0] [0,0,0,1][0, 0, 0, 1] [0,0,1,0][0, 0, 1, 0]
?? 50 [1][1]

s=15s = 15

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12} Sq13Sq^{13} Sq14Sq^{14} Sq15Sq^{15}
P3c0P^3 c_0 32 [1][1] [0][0] [][] [0,0][0, 0] [0,0][0, 0] [0][0] [][] [][] [][] [][] [1][1] [1][1] [][] [][] [1][1] [1][1] [1][1]
P2iP^2 i 39 [1][1] [0,0][0, 0] [0][0] [1,0,1][1, 0, 1] [0,1,1][0, 1, 1] [0,0][0, 0] [0,0][0, 0] [0,0,0][0, 0, 0] [1,0,0][1, 0, 0] [0][0] [0][0] [0][0] [1][1] [0][0] [0][0] [0,1][0, 1] [1][1]
?? 42 [1][1] [0][0] [][] [0][0] [0,0][0, 0] [1,1][1, 1] [1,0][1, 0] [1,0][1, 0] [1,0][1, 0] [0][0] [0][0] [0,0][0, 0] [0,0][0, 0] [1][1] [1,0][1, 0] [1,1][1, 1] [1][1]
?? 54 [1,0][1, 0] [0,0,0][0, 0, 0] [0,0,0][0, 0, 0] [0,0,0,0][0, 0, 0, 0] [0,0,0][0, 0, 0] [0,0,0][0, 0, 0] [0,0][0, 0] [0,0][0, 0] [0,0,0][0, 0, 0] [0,0,1][0, 0, 1] [1,0][1, 0] [1,1][1, 1] [1,1][1, 1] [0,1][0, 1] [1,0,0][1, 0, 0] [1,0,0][1, 0, 0] [1,0][1, 0]

s=16s = 16

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12} Sq13Sq^{13} Sq14Sq^{14} Sq15Sq^{15} Sq16Sq^{16}
P3d0P^3 d_0 38 [1][1] [0][0] [0,0,0][0, 0, 0] [0,1,1][0, 1, 1] [0,0][0, 0] [0,1][0, 1] [0,0,0][0, 0, 0] [1,0,0][1, 0, 0] [0][0] [1][1] [0][0] [1][1] [0][0] [1][1] [0,0][0, 0] [1][1] [0][0] [1][1]
P3e0P^3 e_0 41 [1][1] [][] [0][0] [1,0][1, 0] [1,1][1, 1] [1,0][1, 0] [0,0][0, 0] [0,0][0, 0] [1][1] [1][1] [0,0][0, 0] [0,0][0, 0] [1][1] [1,1][1, 1] [0,1][0, 1] [0][0] [1][1] [1][1]
?? 53 [1,0][1, 0] [0,0,0][0, 0, 0] [0,0,0,0][0, 0, 0, 0] [0,0,0][0, 0, 0] [0,0,0][0, 0, 0] [0,0][0, 0] [0,0][0, 0] [0,1,0][0, 1, 0] [0,0,1][0, 0, 1] [1,0][1, 0] [0,0][0, 0] [0,0][0, 0] [0,0][0, 0] [0,0,0][0, 0, 0] [0,0,1][0, 0, 1] [0,0][0, 0] [1][1] [1][1]

s=17s = 17

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12} Sq13Sq^{13} Sq14Sq^{14} Sq15Sq^{15} Sq16Sq^{16} Sq17Sq^{17}
P4h1P^4 h_1 33 [1][1] [0,0][0, 0] [0,0][0, 0] [0][0] [][] [][] [][] [][] [][] [][] [][] [0][0] [0][0] [0][0] [][] [][] [][] [1][1] [1][1]
P4h2P^4 h_2 35 [1][1] [0][0] [][] [0][0] [0][0] [][] [][] [0][0] [0][0] [][] [][] [][] [][] [0][0] [0][0] [][] [][] [1,0][1, 0] [1][1]
?? 55 [1][1] [0,0,0,0,0][0, 0, 0, 0, 0] [0,0,0,0][0, 0, 0, 0] [0,0,0][0, 0, 0] [0,0][0, 0] [][] [0,0,0][0, 0, 0] [1,0,0,0][1, 0, 0, 0] [0,1,1][0, 1, 1] [0,0][0, 0] [1,1][1, 1] [0,0,0][0, 0, 0] [0,0][0, 0] [0,0][0, 0] [0,0][0, 0] [0,1][0, 1] [1,0][1, 0] [0,1,0][0, 1, 0] [1,1,0][1, 1, 0]

s=19s = 19

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12} Sq13Sq^{13} Sq14Sq^{14} Sq15Sq^{15} Sq16Sq^{16} Sq17Sq^{17} Sq18Sq^{18} Sq19Sq^{19}
P4c0P^4 c_0 40 [1][1] [][] [][] [][] [0,0][0, 0] [0,0][0, 0] [0][0] [0,0][0, 0] [0,0][0, 0] [0][0] [][] [][] [][] [][] [0][0] [0][0] [][] [][] [1][1] [1][1] [1][1]
?? 50 [1][1] [0,0,0][0, 0, 0] [0,0][0, 0] [0,0][0, 0] [0,0,0][0, 0, 0] [0,0,1][0, 0, 1] [1,0][1, 0] [1,1][1, 1] [1,1][1, 1] [0,1][0, 1] [1,0,0][1, 0, 0] [1,0,0][1, 0, 0] [1,0][1, 0] [1][1] [1][1] [1,0][1, 0] [1,0][1, 0] [1][1] [1,1][1, 1] [1,1][1, 1] [1][1]

s=20s = 20

Basis

Name tst - s class Sq0Sq^0 Sq1Sq^1 Sq2Sq^2 Sq3Sq^3 Sq4Sq^4 Sq5Sq^5 Sq6Sq^6 Sq7Sq^7 Sq8Sq^8 Sq9Sq^9 Sq10Sq^{10} Sq11Sq^{11} Sq12Sq^{12} Sq13Sq^{13} Sq14Sq^{14} Sq15Sq^{15} Sq16Sq^{16} Sq17Sq^{17} Sq18Sq^{18} Sq19Sq^{19} Sq20Sq^{20}