SyzygyData

Current Betti Table Entry:

\(n=1\)

\(d=4\)

\(b=1\)

\(p=2\)

\(q=1\)

0 1 2 3
0 2 4 · ·
1 · · 4 2
0 1 2 3
0 (1,0) (4,1) · ·
1 · · (8,5) (9,8)
0 1 2 3
0 1 1 · ·
1 · · 1 1
0 1 2 3
0 1 1 · ·
1 · · 1 1

Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{2,\lambda}(1,1;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{2,1}(1,1;4)\). The dominant weights are displayed in green. Click on an entry for more info!

7 8 9
4 · · ·
5 · 1 ·
6 · · ·

Below is a plot displaying the multigraded Betti numbers. In the \(\textbf{a}=(a_0,a_1)\) spot we place \(\beta_{2,\textbf{a}}(1,1;4)\). Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!

5 6 7 8 9
5 · · · 1 ·
6 · · 1 · ·
7 · 1 · · ·
8 1 · · · ·
9 · · · · ·