New Graph
[2, 3, 1, 2], [4, 4, 4, 3]
π =
[3, 5, 6, 7]
POSSIBLE RANKS
1 x 21
3 x 7
BASE DETERMINANT
17/64, .2656250000
NullSpace of Δ
{1, 2, 3, 4}
Nullspace of A
` det(A) = ` -1/8
1
.
Coloring, {}
R:
[2, 3, 1, 2]
B:
[4, 4, 4, 3]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
4 vs 4 |
4 vs 4 |
3 vs 3 |
2 vs 2 |
Omega Rank for R :
cycles:
{{1, 2, 3}}
order:
3
See Matrix
$ [
[6, 10, 5, 0]
,
[5, 6, 10, 0]
,
[10, 5, 6, 0]
] $
[y3, y1, y2, 0]
Omega Rank for B :
cycles:
{{3, 4}}
order:
2
See Matrix
$ [
[0, 0, 7, 14]
,
[0, 0, 14, 7]
] $
[0, 0, y2, y1]
2
.
Coloring, {2}
R:
[2, 4, 1, 2]
B:
[4, 3, 4, 3]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
3 vs 4 |
4 vs 4 |
3 vs 3 |
2 vs 2 |
Omega Rank for R :
cycles:
{{2, 4}}
order:
2
See Matrix
$ [
[6, 10, 0, 5]
,
[0, 11, 0, 10]
,
[0, 10, 0, 11]
] $
[y1, y2, 0, y3]
Omega Rank for B :
cycles:
{{3, 4}}
order:
2
See Matrix
$ [
[0, 0, 12, 9]
,
[0, 0, 9, 12]
] $
[0, 0, y1, y2]
3
.
Coloring, {3}
R:
[2, 3, 4, 2]
B:
[4, 4, 1, 3]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
4 vs 4 |
4 vs 4 |
3 vs 3 |
3 vs 3 |
Omega Rank for R :
cycles:
{{2, 3, 4}}
order:
3
See Matrix
$ [
[0, 10, 5, 6]
,
[0, 6, 10, 5]
,
[0, 5, 6, 10]
] $
[0, y1, y2, y3]
Omega Rank for B :
cycles:
{{1, 3, 4}}
order:
3
See Matrix
$ [
[6, 0, 7, 8]
,
[7, 0, 8, 6]
,
[8, 0, 6, 7]
] $
[y1, 0, y2, y3]
4
.
Coloring, {4}
R:
[2, 3, 1, 3]
B:
[4, 4, 4, 2]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
4 vs 4 |
4 vs 4 |
3 vs 3 |
2 vs 2 |
Omega Rank for R :
cycles:
{{1, 2, 3}}
order:
3
See Matrix
$ [
[6, 3, 12, 0]
,
[12, 6, 3, 0]
,
[3, 12, 6, 0]
] $
[y3, y1, y2, 0]
Omega Rank for B :
cycles:
{{2, 4}}
order:
2
See Matrix
$ [
[0, 7, 0, 14]
,
[0, 14, 0, 7]
] $
[0, y1, 0, y2]
5
.
Coloring, {2, 3}
R:
[2, 4, 4, 2]
B:
[4, 3, 1, 3]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
4 vs 4 |
4 vs 4 |
2 vs 2 |
3 vs 3 |
Omega Rank for R :
cycles:
{{2, 4}}
order:
2
See Matrix
$ [
[0, 10, 0, 11]
,
[0, 11, 0, 10]
] $
[0, y1, 0, y2]
Omega Rank for B :
cycles:
{{1, 3, 4}}
order:
3
See Matrix
$ [
[6, 0, 12, 3]
,
[12, 0, 3, 6]
,
[3, 0, 6, 12]
] $
[y1, 0, y2, y3]
6
.
Coloring, {2, 4}
R:
[2, 4, 1, 3]
B:
[4, 3, 4, 2]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
3 vs 4 |
4 vs 4 |
4 vs 4 |
3 vs 3 |
Omega Rank for R :
cycles:
{{1, 2, 3, 4}}
order:
4
See Matrix
$ [
[6, 3, 7, 5]
,
[7, 6, 5, 3]
,
[5, 7, 3, 6]
,
[3, 5, 6, 7]
] $
[y2, y1, y3, y4]
Omega Rank for B :
cycles:
{{2, 3, 4}}
order:
3
See Matrix
$ [
[0, 7, 5, 9]
,
[0, 9, 7, 5]
,
[0, 5, 9, 7]
] $
[0, y3, y1, y2]
7
.
Coloring, {3, 4}
R:
[2, 3, 4, 3]
B:
[4, 4, 1, 2]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
4 vs 4 |
4 vs 4 |
3 vs 3 |
3 vs 3 |
Omega Rank for R :
cycles:
{{3, 4}}
order:
2
See Matrix
$ [
[0, 3, 12, 6]
,
[0, 0, 9, 12]
,
[0, 0, 12, 9]
] $
[0, y3, y2, y1]
Omega Rank for B :
cycles:
{{2, 4}}
order:
2
See Matrix
$ [
[6, 7, 0, 8]
,
[0, 8, 0, 13]
,
[0, 13, 0, 8]
] $
[y1, y2, 0, y3]
8
.
Coloring, {2, 3, 4}
R:
[2, 4, 4, 3]
B:
[4, 3, 1, 2]
` See graph `
` See pair graph `
| Δ-Rank | A+(1/2)Δ |
A-(1/2)Δ | R | B |
| 3 vs 3 |
4 vs 4 |
4 vs 4 |
3 vs 3 |
4 vs 4 |
Omega Rank for R :
cycles:
{{3, 4}}
order:
2
See Matrix
$ [
[0, 3, 7, 11]
,
[0, 0, 11, 10]
,
[0, 0, 10, 11]
] $
[0, y1, y2, y3]
Omega Rank for B :
cycles:
{{1, 2, 3, 4}}
order:
4
See Matrix
$ [
[6, 7, 5, 3]
,
[5, 3, 7, 6]
,
[7, 6, 3, 5]
,
[3, 5, 6, 7]
] $
[y1, y3, y4, y2]
| SUMMARY |
|---|
| Graph Type |
| NOT CC |
|---|
| ν(A) |
|
0
|
|---|
| ν(Δ) |
|
1
|
|---|
| π |
|
[3, 5, 6, 7]
|
|---|
| Dbly Stoch |
| false |
|---|
| SANDWICH |
| Total
0
|
|---|
| No . | Coloring | Rank |
|---|
| RT GROUPS |
| Total
0
|
|---|
| No . | Coloring | Rank | Solv |
|---|
| Δ-RANK'D | SC'D !RK'D |
τ-RANK'D | R/B RANK'D | NOT SYNC'D |
Total Runs | 2n-1 |
|---|
| 8 |
0 |
6 , 8 |
8 , 8 |
0 |
8 |
8 |