SyzygyData

Current Betti Table Entry:

\(n=1\)

\(d=9\)

\(b=7\)

\(p=8\)

\(q=1\)

0 1 2 3 4 5 6 7 8
0 8 63 216 420 504 378 168 36 ·
1 · · · · · · · · 1
0 1 2 3 4 5 6 7 8
0 (7,0) (15,1) (22,3) (28,6) (33,10) (37,15) (40,21) (42,28) ·
1 · · · · · · · · (44,44)
0 1 2 3 4 5 6 7 8
0 1 1 1 1 1 1 1 1 ·
1 · · · · · · · · 1
0 1 2 3 4 5 6 7 8
0 1 1 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 \(\beta_{8,\lambda}(1,7;9)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{8,1}(1,7;9)\). The dominant weights are displayed in green. Click on an entry for more info!

43 44 45
43 · · ·
44 · 1 ·
45 · · ·

Below is a plot displaying the multigraded Betti numbers. In the \(\textbf{a}=(a_0,a_1)\) spot we place \(\beta_{8,\textbf{a}}(1,7;9)\). Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!

44 45
44 1 ·
45 · ·