On Erdős conjecture for multiplicities

Antoine Deza, Frantisek Franek, and Min Jing Liu
Advanced Optimization Laboratory
Department of Computing and Software
McMaster University, Hamilton, Ontario, Canada

C_8

 

c_8

Pattern

|X|=8

|X|=9

|X|=10

|X|=11

|X|=12

|X|=13

3 4 7 8

0011001100

128.253372

8.74427414

0.984893

1.469739

0.764096

1.482639

 

 

47.0188292

9.89135676

2.907046

2.907046

1.136675

1.698777

1,3,4,7,8

1011001100

177.349806

11.698255

1.144828

1.24099

0.727891

1.412798

 

 

30.5008442

6.02887988

2.064356

2.328643

1.008339

1.59025

3,4,7,8,9

00110011100

 

8.74427414

1.144828

1.694184

4.852246

25.47853

 

 

 

9.89135676

2.064356

1.231851

2.943325

21.5456

1,3,4,7,8,9

1011001110

 

11.6982784

1.73553

2.451886

6.419867

28.53269

 

 

 

6.02887988

1.509761

1.384076

4.051191

25.17843

3,4,7,8,10

0011001101

 

0.998159

1.24099

1.018382

2.563385

 

 

 

2.807956

2.328643

0.894851

2.049874

3,4,7,8,9,10

0011001111

 

 

1.163795

2.451886

9.221715

 

 

 

 

 

1.996628

1.384076

5.847909

 

1,3,4,7,8,10

1011001101

 

 

1.163795

1.154132

1.037657

2.612897

 

 

 

 

1.996628

1.996628

0.84958

2.075237

1,3,4,7,8,9,10

1011001111

 

 

1.793531

4.044395

12.46608

 

 

 

 

 

1.448659

2.086485

8.281844

 

 

 

3,4,7,8,11

00110011001

 

 

 

0.984893

0.711223

1.320089

 

 

 

 

 

1.517832

0.994211

1.351412

3,4,7,8,9,11

00110011101

 

 

 

2.460246

6.176354

37.48498

 

 

 

 

 

1.328202

3.84977

32.16709

3,4,7,8,10,11

00110011011

 

 

 

1.028991

1.078708

3.669519

 

 

 

 

 

1.305992

0.838105

2.90612

3,4,7,8,9,10,11

00110011111

 

 

 

3.495819

12.23673

142.8636

 

 

 

 

 

1.736346

8.079113

128.6108

1,3,4,7,8,11

10110011001

 

 

 

1.028991

0.703381

1.329367

 

 

 

 

 

1.305992

0.904479

1.331959

1,3,4,7,8,9,11

10110011101

 

 

 

3.495819

7.942877

41.45145

 

 

 

 

 

1.736346

5.127293

36.65099

1,3,4,7,8,10,11

10110011011

 

 

 

1.163795

1.128187

3.795929

 

 

 

 

 

1.175185

0.818836

3.001171

1,3,4,7,8,9,10,11

10110011111

 

 

 

5.765365

16.646

165.2249

 

 

 

 

 

2.933887

11.49518

149.4055

 

 

3,4,7,8,12

001100110001

 

 

 

 

0.759071

1.429196

 

 

 

 

 

 

1.123802

1.613629

3,4,7,8,9,12

001100111001

 

 

 

 

4.984104

 

 

 

 

 

 

 

3.027281

 

3,4,7,8,10,12

001100110101

 

 

 

 

1.026154

2.766659

 

 

 

 

 

 

0.896881

2.192284

3,4,7,8,11,12

001100110011

 

 

 

 

0.707435

1.332869

 

 

 

 

 

 

0.983358

1.33314

3,4,7,8,9,10,12

001100111101

 

 

 

 

9.453802

 

 

 

 

 

 

 

6.017537

 

3,4,7,8,9,11,12

001100111011

 

 

 

 

6.329715

 

 

 

 

 

 

 

3.951571

 

3,4,7,8,10,11,12

001100110111

 

 

 

 

1.086864

4.020851

 

 

 

 

 

 

0.840857

3.183348

3,4,7,8,9,10,11,12

001100111111

 

 

 

 

12.5112

 

 

 

 

 

 

 

8.284836

 

1,3,4,7,8,12

101100110001

 

 

 

 

0.724103

1.365484

 

 

 

 

 

 

0.997486

1.512575

1,3,4,7,8,9,12

101100111001

 

 

 

 

6.576328

29.69793

 

 

 

 

 

 

4.155753

26.20148

1,3,4,7,8,10,12

101100110101

 

 

 

 

1.045811

2.817358

 

 

 

 

 

 

0.852332

2.224119

1,3,4,7,8,11,12

101100110011

 

 

 

 

0.700141

1.34578

 

 

 

 

 

 

0.893859

1.316484

1,3,4,7,8,9,10,12

101100111101

 

 

 

 

12.7411

 

 

 

 

 

 

 

8.488036

 

1,3,4,7,8,9,11,12

101100111011

 

 

 

 

8.190257

 

 

 

 

 

 

 

5.306228

 

1,3,4,7,8,10,11,12

101100110111

 

 

 

 

1.137086

4.161823

 

 

 

 

 

 

0.821946

3.290568

1,3,4,7,8,9,10,11,12

101100111111

 

 

 

 

17.09949

 

 

 

 

 

 

 

11.85324

 

 

 

3,4,7,8,13

0011001100001

 

 

 

 

 

1.482639

 

 

 

 

 

 

 

1.698777

3,4,7,8,10,13

0011001101001

 

 

 

 

 

2.563387

 

 

 

 

 

 

 

2.044988

3,4,7,8,11,13

0011001100101

 

 

 

 

 

1.320089

 

 

 

 

 

 

 

1.351425

3,4,7,8,12,13

0011001100011

 

 

 

 

 

1.429196

 

 

 

 

 

 

 

1.613629

3,4,7,8,10,11,13

0011001101101

 

 

 

 

 

3.669522

 

 

 

 

 

 

 

2.906121

3,4,7,8,10,11,12,13

0011001101111

 

 

 

 

 

4.020053

 

 

 

 

 

 

 

3.183349

1,3,4,7,8,13

1011001100001

 

 

 

 

 

1.412798

 

 

 

 

 

 

 

1.59025

1,3,4,7,8,10,13

1011001101001

 

 

 

 

 

2.612899

 

 

 

 

 

 

 

2.075238

1,3,4,7,8,11,13

1011001100101

 

 

 

 

 

1.329367

 

 

 

 

 

 

 

1.331959

1,3,4,7,8,12,13

1011001100011

 

 

 

 

 

1.365484

 

 

 

 

 

 

 

1.512574

1,3,4,7,8,10,11,13

1011001101101

 

 

 

 

 

3.795931

 

 

 

 

 

 

 

3.001172

1,3,4,7,8,10,11,12,13

1011001101111

 

 

 

 

 

4.161827

 

 

 

 

 

 

 

3.290569