SyzygyData

Current Betti Table Entry:

\(n=1\)

\(d=7\)

\(b=2\)

\(p=0\)

\(q=0\)

0 1 2 3 4 5 6
0 3 14 21 · · · ·
1 · · · 35 42 21 4
0 1 2 3 4 5 6
0 (2,0) (8,1) (13,3) · · · ·
1 · · · (21,9) (24,13) (26,18) (27,24)
0 1 2 3 4 5 6
0 1 1 1 · · · ·
1 · · · 1 1 1 1
0 1 2 3 4 5 6
0 1 1 1 · · · ·
1 · · · 1 1 1 1

Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{0,\lambda}(1,2;7)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{0,0}(1,2;7)\). The dominant weights are displayed in green. Click on an entry for more info!

1 2 3
-1 · · ·
0 · 1 ·
1 · · ·

Below is a plot displaying the multigraded Betti numbers. In the \(\textbf{a}=(a_0,a_1)\) spot we place \(\beta_{0,\textbf{a}}(1,2;7)\). Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!

0 1 2 3
0 · · 1 ·
1 · 1 · ·
2 1 · · ·
3 · · · ·