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

We tried to compute 1 million Frobenius elements for each of the primes 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 72,
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	1009	5003	10007	30011
(6)	12.0656	12.0075	11.9929	12.0146
(3,3)	4.0223	3.9935	4.0162	3.9713
(2,4)	18.0475	17.9813	18.0396	17.9603
(2,2,2)	6.0154	6.0132	6.0103	6.0280
(1,2,3)	11.9587	12.0321	11.9848	11.9977
(1,1,2,2)	8.9961	8.9630	8.9815	8.9924
(1,1,1,3)	3.9460	4.0101	4.0062	4.0059
(1,1,1,1,2)	5.9637	5.9916	5.9783	6.0218
(1,1,1,1,1,1)	0.9847	1.0077	0.9901	1.0079

Cycles found in 990177 samples			Prime 1009
Cycle Type	Frequency	Fraction	Empirical
(6)	165932	12.0656	12.25
(3,3)	55316	4.0223	4.08
(2,4)	248198	18.0475	18.33
(2,2,2)	82727	6.0154	6.11
(1,2,3)	164462	11.9587	12.14
(1,1,2,2)	123718	8.9961	9.14
(1,1,1,3)	54267	3.9460	4.01
(1,1,1,1,2)	82015	5.9637	6.06
(1,1,1,1,1,1)	13542	0.9847	1.00

Cycles found in 998075 samples			Prime 5003
Cycle Type	Frequency	Fraction	Empirical
(6)	166450	12.0075	11.92
(3,3)	55358	3.9935	3.96
(2,4)	249259	17.9813	17.84
(2,2,2)	83356	6.0132	5.97
(1,2,3)	166791	12.0321	11.94
(1,1,2,2)	124247	8.9630	8.89
(1,1,1,3)	55589	4.0101	3.98
(1,1,1,1,2)	83056	5.9916	5.95
(1,1,1,1,1,1)	13969	1.0077	1.00

Cycles found in 998970 samples			Prime 10007
Cycle Type	Frequency	Fraction	Empirical
(6)	166397	11.9929	12.11
(3,3)	55723	4.0162	4.06
(2,4)	250292	18.0396	18.22
(2,2,2)	83390	6.0103	6.07
(1,2,3)	166284	11.9848	12.10
(1,1,2,2)	124615	8.9815	9.07
(1,1,1,3)	55585	4.0062	4.05
(1,1,1,1,2)	82947	5.9783	6.04
(1,1,1,1,1,1)	13737	0.9901	1.00

Cycles found in 999695 samples			Prime 30011
Cycle Type	Frequency	Fraction	Empirical
(6)	166819	12.0146	11.92
(3,3)	55140	3.9713	3.94
(2,4)	249372	17.9603	17.82
(2,2,2)	83697	6.0280	5.98
(1,2,3)	166584	11.9977	11.90
(1,1,2,2)	124857	8.9924	8.92
(1,1,1,3)	55621	4.0059	3.97
(1,1,1,1,2)	83610	6.0218	5.97
(1,1,1,1,1,1)	13995	1.0079	1.00

Last modified: Fri Oct 19 17:12:23 CDT 2018