SyzygyData

Current Betti Table Entry:

\(n=1\)

\(d=3\)

\(b=2\)

\(p=1\)

\(q=0\)

0 1 2
0 3 6 3
1 · · ·
0 1 2
0 (2,0) (4,1) (5,3)
1 · · ·
0 1 2
0 1 1 1
1 · · ·
0 1 2
0 1 1 1
1 · · ·

Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{1,\lambda}(1,2;3)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{1,0}(1,2;3)\). The dominant weights are displayed in green. Click on an entry for more info!

3 4 5
0 · · ·
1 · 1 ·
2 · · ·

Below is a plot displaying the multigraded Betti numbers. In the \(\textbf{a}=(a_0,a_1)\) spot we place \(\beta_{1,\textbf{a}}(1,2;3)\). Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!

1 2 3 4 5
1 · · · 1 ·
2 · · 2 · ·
3 · 2 · · ·
4 1 · · · ·
5 · · · · ·