Wiki
Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
erdos_699_index_8_curve_obstruction.json
json
{
"index": 8,
"denominator": 100,
"selected_positions_in_prime_order_2_3_5_7": [
1,
3,
0,
2
],
"cofactor_exponents": [
"3/10",
"3/10",
"3/10",
"3/10"
],
"row_capacities": [
"3/10",
"3/10",
"3/10",
"3/10",
"1",
"1",
"1",
"1"
],
"points": [
{
"point": [
0,
0
],
"weight_numerator": 30,
"cover_numerator": 30
},
{
"point": [
0,
1
],
"weight_numerator": 15,
"cover_numerator": 15
},
{
"point": [
1,
0
],
"weight_numerator": 15,
"cover_numerator": 15
},
{
"point": [
0,
2
],
"weight_numerator": 11,
"cover_numerator": 13
},
{
"point": [
1,
1
],
"weight_numerator": 8,
"cover_numerator": 28
},
{
"point": [
2,
0
],
"weight_numerator": 11,
"cover_numerator": 13
},
{
"point": [
0,
3
],
"weight_numerator": 3,
"cover_numerator": 14
},
{
"point": [
1,
2
],
"weight_numerator": 12,
"cover_numerator": 12
},
{
"point": [
2,
1
],
"weight_numerator": 12,
"cover_numerator": 12
},
{
"point": [
3,
0
],
"weight_numerator": 3,
"cover_numerator": 14
},
{
"point": [
0,
4
],
"weight_numerator": 15,
"cover_numerator": 15
},
{
"point": [
1,
3
],
"weight_numerator": 20,
"cover_numerator": 20
},
{
"point": [
2,
2
],
"weight_numerator": 30,
"cover_numerator": 31
},
{
"point": [
3,
1
],
"weight_numerator": 20,
"cover_numerator": 20
},
{
"point": [
4,
0
],
"weight_numerator": 15,
"cover_numerator": 15
},
{
"point": [
0,
5
],
"weight_numerator": 16,
"cover_numerator": 16
},
{
"point": [
1,
4
],
"weight_numerator": 15,
"cover_numerator": 15
},
{
"point": [
2,
3
],
"weight_numerator": 19,
"cover_numerator": 19
},
{
"point": [
3,
2
],
"weight_numerator": 19,
"cover_numerator": 19
},
{
"point": [
4,
1
],
"weight_numerator": 15,
"cover_numerator": 15
},
{
"point": [
5,
0
],
"weight_numerator": 16,
"cover_numerator": 16
},
{
"point": [
0,
6
],
"weight_numerator": 10,
"cover_numerator": 14
},
{
"point": [
1,
5
],
"weight_numerator": 13,
"cover_numerator": 13
},
{
"point": [
2,
4
],
"weight_numerator": 11,
"cover_numerator": 11
},
{
"point": [
3,
3
],
"weight_numerator": 32,
"cover_numerator": 32
},
{
"point": [
4,
2
],
"weight_numerator": 11,
"cover_numerator": 11
},
{
"point": [
5,
1
],
"weight_numerator": 13,
"cover_numerator": 13
},
{
"point": [
6,
0
],
"weight_numerator": 10,
"cover_numerator": 14
},
{
"point": [
0,
7
],
"weight_numerator": 0,
"cover_numerator": 19
},
{
"point": [
1,
6
],
"weight_numerator": 17,
"cover_numerator": 18
},
{
"point": [
2,
5
],
"weight_numerator": 16,
"cover_numerator": 16
},
{
"point": [
3,
4
],
"weight_numerator": 17,
"cover_numerator": 17
},
{
"point": [
4,
3
],
"weight_numerator": 17,
"cover_numerator": 17
},
{
"point": [
5,
2
],
"weight_numerator": 16,
"cover_numerator": 16
},
{
"point": [
6,
1
],
"weight_numerator": 17,
"cover_numerator": 18
},
{
"point": [
7,
0
],
"weight_numerator": 0,
"cover_numerator": 19
}
],
"line_cover": [
{
"coefficients": [
1,
0,
0
],
"cover_numerator": 8,
"own_incidence_numerator": 100
},
{
"coefficients": [
0,
1,
0
],
"cover_numerator": 8,
"own_incidence_numerator": 100
},
{
"coefficients": [
1,
0,
-1
],
"cover_numerator": 7,
"own_incidence_numerator": 100
},
{
"coefficients": [
0,
1,
-1
],
"cover_numerator": 7,
"own_incidence_numerator": 100
},
{
"coefficients": [
1,
0,
-2
],
"cover_numerator": 5,
"own_incidence_numerator": 99
},
{
"coefficients": [
0,
1,
-2
],
"cover_numerator": 5,
"own_incidence_numerator": 99
},
{
"coefficients": [
1,
0,
-3
],
"cover_numerator": 6,
"own_incidence_numerator": 91
},
{
"coefficients": [
0,
1,
-3
],
"cover_numerator": 6,
"own_incidence_numerator": 91
},
{
"coefficients": [
1,
1,
-4
],
"cover_numerator": 7,
"own_incidence_numerator": 100
},
{
"coefficients": [
1,
1,
-5
],
"cover_numerator": 8,
"own_incidence_numerator": 100
},
{
"coefficients": [
1,
1,
-6
],
"cover_numerator": 6,
"own_incidence_numerator": 100
},
{
"coefficients": [
1,
1,
-7
],
"cover_numerator": 11,
"own_incidence_numerator": 100
},
{
"coefficients": [
1,
-1,
0
],
"cover_numerator": 14,
"own_incidence_numerator": 100
}
],
"cover_total": "49/50",
"universal_polynomial_inequality": "sum_P w_P ord_P(F) <= deg(F) for every nonzero complex polynomial F",
"row_multiplicity_consequence": "deg(F) >= 3/10*(m0+m1+m2+m3)+m4+m5+m6+m7",
"noncover_irreducible_bound": "sum_P w_P mult_P(C) <= 49/50*deg(C)",
"scope": "An obstruction to strict weighted-multiplicity versus total-degree gain at this cofactor profile; no bad triple or whole-index result is claimed."
}
Graph