A053725
Number of n X n binary matrices of order dividing 3 (also number of solutions to X^3=I in GL(n,2)).
Original entry on oeis.org
1, 3, 57, 1233, 75393, 19109889, 6326835201, 6388287561729, 23576681450405889, 120906321631678693377, 1968421511613895105052673, 111055505036706392268074909697, 8965464105556083354144035638870017
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
-
\\ See Morison theorem 2.6
\\ F(n,q,k) is number of solutions to X^k=I in GL(i, GF(q)) for i=1..n.
\\ q is power of prime and gcd(q, k) = 1.
B(n,q,e)={sum(m=0, n\e, x^(m*e)/prod(k=0, m-1, q^(m*e)-q^(k*e)))}
F(n,q,k)={if(gcd(q,k)<>1, error("no can do")); my(D=ffgen(q)^0); my(f=factor(D*(x^k-1))); my(p=prod(i=1, #f~, (B(n, q, poldegree(f[i,1])) + O(x*x^n))^f[i,2])); my(r=B(n,q,1)); vector(n, i, polcoeff(p, i)/polcoeff(r, i))}
F(10, 2, 3) \\ Andrew Howroyd, Jul 09 2018
A063393
Number of solutions of x^10=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 10, 92, 23200, 21391520, 35841831040, 95709758320640, 6206883395497062400, 1502803598296957497344000, 654083813715060854940290252800, 450433384822340709737677746549555200
Offset: 1
A063385
Number of solutions of x^2=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 10, 92, 1696, 59552, 4124800, 556101632, 148425895936, 78099471368192, 81705857229783040, 169694608681978560512, 702657511446831375056896, 5797142351555426979908943872, 95500953266115919784543392890880, 3140561514292519005433439594146168832
Offset: 1
A053770
Number of n X n binary matrices of order dividing 5 (i.e., number of solutions of X^5=I in GL(n,2)).
Original entry on oeis.org
1, 1, 1, 1345, 666625, 223985665, 65019838465, 105072058957825, 11436238073940148225, 997931868985434228916225, 74706800043914446529756135425, 5321514758546715999509008953114625, 3721818216683598164434468712927276826625
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053777
Number of n X n binary matrices of order dividing 12 (i.e., number of solutions of X^12=I in GL(n,2)).
Original entry on oeis.org
1, 6, 120, 10368, 2582208, 3143720448, 11692182896640, 219197554267521024, 12804488375721592356864, 3325324798296500862330077184, 2537067900325971750395878897090560, 8900626797123384385697033838119859781632, 65799342288255766009804607851267459830106816512
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053771
Number of n X n binary matrices of order dividing 6 (i.e., number of solutions of X^6=I in GL(n,2)).
Original entry on oeis.org
1, 6, 78, 6588, 1332288, 1335398688, 2230748717184, 13819713971871744, 219439188546028498944, 16360198814356838801178624, 3333281205541847127897252298752, 2704161270841324410691567986117967872
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053773
Number of n X n binary matrices of order dividing 8 (i.e., number of solutions of X^8=I in GL(n,2)).
Original entry on oeis.org
1, 1, 4, 64, 4096, 1048576, 1073741824, 4398046511104, 72057594037927936, 1989505896802466922496, 164384949539438492410445824, 47902612878717208996830483841024
Offset: 0
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A062250
Number of cyclic subgroups of Chevalley group A_n(2) (the group of nonsingular n X n matrices over GF(2) ).
Original entry on oeis.org
1, 5, 79, 6974, 2037136, 2890467344, 14011554132032, 325330342132674560, 27173394819858612320256, 10158190320726534408118452224, 13156630408268153048253765001412608, 80280189722884518774834501142737770774528
Offset: 1
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 01 2001
a(3) = 1/phi(1)+21/phi(2)+56/phi(3)+42/phi(4)+48/phi(7) = 79.
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A063386
Number of solutions of x^3=1 in general affine group AGL(n,2).
Original entry on oeis.org
1, 9, 225, 6273, 968193, 307091457, 144510377985, 338450286215169, 1535613392752345089, 11693653105154832465921, 423384155808298738368118785, 29155340360444250715547947237377
Offset: 1
A053772
Number of n X n binary matrices of order dividing 7 (i.e., number of solutions of X^7=I in GL(n,2)).
Original entry on oeis.org
1, 1, 49, 5761, 476161, 457113601, 3439085027329, 18696142934507521, 144017748317668638721, 30063679011292374997401601, 10371304522603231166854078660609, 3639433320096084212920229480292679681, 18767347744724322162378748108305552459694081
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
Showing 1-10 of 23 results.