matroid #1
- n
- 10
- rank
- 5
- bases
- 136
- α(M)
- 8/7 ≈ 1.1429
Description (matrix) GF(2)
[[1,0,1,0,1,0,1,0,1,0], [0,1,1,1,0,0,0,0,0,0], [0,1,0,0,1,1,0,0,0,0], [0,1,0,0,0,0,1,1,0,0], [0,1,0,0,0,0,0,0,1,1]]
show all 136 bases
[[0,1,2,4,6], [0,1,3,4,6], [1,2,3,4,6], [0,1,2,5,6], [0,1,3,5,6], [1,2,3,5,6], [1,2,4,5,6], [1,3,4,5,6], [0,1,2,4,7], [0,1,3,4,7], [1,2,3,4,7], [0,1,2,5,7], [0,1,3,5,7], [1,2,3,5,7], [1,2,4,5,7], [1,3,4,5,7], [1,2,4,6,7], [1,3,4,6,7], [1,2,5,6,7], [1,3,5,6,7], [0,1,2,4,8], [0,1,3,4,8], [1,2,3,4,8], [0,1,2,5,8], [0,1,3,5,8], [1,2,3,5,8], [1,2,4,5,8], [1,3,4,5,8], [0,1,2,6,8], [0,1,3,6,8], [1,2,3,6,8], [0,1,4,6,8], [0,2,4,6,8], [0,3,4,6,8], [1,3,4,6,8], [2,3,4,6,8], [0,1,5,6,8], [0,2,5,6,8], [1,2,5,6,8], [0,3,5,6,8], [2,3,5,6,8], [1,4,5,6,8], [2,4,5,6,8], [3,4,5,6,8], [0,1,2,7,8], [0,1,3,7,8], [1,2,3,7,8], [0,1,4,7,8], [0,2,4,7,8], [1,2,4,7,8], [0,3,4,7,8], [2,3,4,7,8], [0,1,5,7,8], [0,2,5,7,8], [0,3,5,7,8], [1,3,5,7,8], [2,3,5,7,8], [1,4,5,7,8], [2,4,5,7,8], [3,4,5,7,8], [1,2,6,7,8], [1,3,6,7,8], [1,4,6,7,8], [2,4,6,7,8], [3,4,6,7,8], [1,5,6,7,8], [2,5,6,7,8], [3,5,6,7,8], [0,1,2,4,9], [0,1,3,4,9], [1,2,3,4,9], [0,1,2,5,9], [0,1,3,5,9], [1,2,3,5,9], [1,2,4,5,9], [1,3,4,5,9], [0,1,2,6,9], [0,1,3,6,9], [1,2,3,6,9], [0,1,4,6,9], [0,2,4,6,9], [1,2,4,6,9], [0,3,4,6,9], [2,3,4,6,9], [0,1,5,6,9], [0,2,5,6,9], [0,3,5,6,9], [1,3,5,6,9], [2,3,5,6,9], [1,4,5,6,9], [2,4,5,6,9], [3,4,5,6,9], [0,1,2,7,9], [0,1,3,7,9], [1,2,3,7,9], [0,1,4,7,9], [0,2,4,7,9], [0,3,4,7,9], [1,3,4,7,9], [2,3,4,7,9], [0,1,5,7,9], [0,2,5,7,9], [1,2,5,7,9], [0,3,5,7,9], [2,3,5,7,9], [1,4,5,7,9], [2,4,5,7,9], [3,4,5,7,9], [1,2,6,7,9], [1,3,6,7,9], [1,4,6,7,9], [2,4,6,7,9], [3,4,6,7,9], [1,5,6,7,9], [2,5,6,7,9], [3,5,6,7,9], [1,2,4,8,9], [1,3,4,8,9], [1,2,5,8,9], [1,3,5,8,9], [1,2,6,8,9], [1,3,6,8,9], [1,4,6,8,9], [2,4,6,8,9], [3,4,6,8,9], [1,5,6,8,9], [2,5,6,8,9], [3,5,6,8,9], [1,2,7,8,9], [1,3,7,8,9], [1,4,7,8,9], [2,4,7,8,9], [3,4,7,8,9], [1,5,7,8,9], [2,5,7,8,9], [3,5,7,8,9]]
Maximizing pair
(0, 1); basis counts at (i, j) = (0, 1):
| j ∈ B | j ∉ B | |
|---|---|---|
| i ∈ B | 32 | 16 |
| i ∉ B | 56 | 32 |
Attribution
The finite-field spike M_2^5 of Huh, Schroter, and Wang (Correlation bounds for fields and matroids, arXiv:1806.02675, Definition 19; discovered June 2018, no AI use reported in that record). Columns over GF(2): the tip e1, the vector e2+e3+e4+e5, and k*e1+e_m for m=2..5, k=1..p. Submitted from the literature.
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