Frobenius elements for = 6 on G(4,9).

We tried to compute 300000 Frobenius elements for each of the primes 101, 1009, 5003, 10007, and 30011
for the enriched Schubert problem

= 6 on G(4,9).
For each cycle type and prime, we record the number observed (frequency), the fraction, normalised to 48,
and an empirical fraction, where we divide the frequency by number of times the identity was observed.
The first table compares the observed fraction at the different primes, and later tables are for the computations at each prime.

Fractions found at different primes
Cycle Type	101	1009	5003	10007	30011
(6)	8.3680	8.0142	8.0453	8.0230	7.9468
(3,3)	8.4161	8.0447	8.0541	8.0204	7.9534
(2,4)	5.9987	5.9721	5.9320	5.9862	6.0280
(2,2,2)	6.7780	6.9972	6.9955	6.9843	7.0091
(1,1,4)	6.0537	6.0143	6.0044	5.9995	6.0179
(1,1,2,2)	8.7784	8.9946	8.9827	8.9988	9.0208
(1,1,1,1,2)	2.7555	2.9677	3.0105	3.0036	2.9938
(1,1,1,1,1,1)	0.8516	0.9952	0.9754	0.9843	1.0301

Cycles found in 273859 samples			Prime 101
Cycle Type	Frequency	Fraction	Empirical
(6)	47743	8.3680	9.83
(3,3)	48017	8.4161	9.88
(2,4)	34225	5.9987	7.04
(2,2,2)	38671	6.7780	7.96
(1,1,4)	34539	6.0537	7.11
(1,1,2,2)	50084	8.7784	10.31
(1,1,1,1,2)	15721	2.7555	3.24
(1,1,1,1,1,1)	4859	0.8516	1.00

Cycles found in 297300 samples			Prime 1009
Cycle Type	Frequency	Fraction	Empirical
(6)	49638	8.0142	8.05
(3,3)	49827	8.0447	8.08
(2,4)	36990	5.9721	6.00
(2,2,2)	43339	6.9972	7.03
(1,1,4)	37251	6.0143	6.04
(1,1,2,2)	55710	8.9946	9.04
(1,1,1,1,2)	18381	2.9677	2.98
(1,1,1,1,1,1)	6164	0.9952	1.00

Cycles found in 299444 samples			Prime 5003
Cycle Type	Frequency	Fraction	Empirical
(6)	50190	8.0453	8.25
(3,3)	50245	8.0541	8.26
(2,4)	37006	5.9320	6.08
(2,2,2)	43641	6.9955	7.17
(1,1,4)	37458	6.0044	6.16
(1,1,2,2)	56038	8.9827	9.21
(1,1,1,1,2)	18781	3.0105	3.09
(1,1,1,1,1,1)	6085	0.9754	1.00

Cycles found in 299721 samples			Prime 10007
Cycle Type	Frequency	Fraction	Empirical
(6)	50097	8.0230	8.15
(3,3)	50081	8.0204	8.15
(2,4)	37379	5.9862	6.08
(2,2,2)	43611	6.9843	7.10
(1,1,4)	37462	5.9995	6.10
(1,1,2,2)	56190	8.9988	9.14
(1,1,1,1,2)	18755	3.0036	3.05
(1,1,1,1,1,1)	6146	0.9843	1.00

Cycles found in 299911 samples			Prime 30011
Cycle Type	Frequency	Fraction	Empirical
(6)	49653	7.9468	7.71
(3,3)	49694	7.9534	7.72
(2,4)	37664	6.0280	5.85
(2,2,2)	43794	7.0091	6.80
(1,1,4)	37601	6.0179	5.84
(1,1,2,2)	56363	9.0208	8.76
(1,1,1,1,2)	18706	2.9938	2.91
(1,1,1,1,1,1)	6436	1.0301	1.00

Last modified: Fri Nov 2 21:01:32 EDT 2018