A089035
Number of n X n matrices over GF(2) with characteristic polynomial x^n - 1.
Original entry on oeis.org
1, 4, 56, 4096, 666624, 1194590208, 3343877406720, 72057594037927936, 3701652434038082764800, 1021880992906173430024372224, 750836199529096452135514747699200, 7415506491123333639280491668337906941952, 52777360037873674206622083843242895013104844800
Offset: 1
Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003
-
\\ see Reiner reference.
F(u,r)={prod(i=1, r, (1-u^(-i)))}
a(n, q=2)={my(D=ffgen(q)); my(f=factor(D^0*(x^n-1))); q^(n^2-n)*F(q,n)/prod(i=1, #f~, F(q^poldegree(f[i,1]), f[i,2]))} \\ Andrew Howroyd, Jul 08 2018
A088654
Number of n X n matrices over GF(4) with characteristic polynomial x^n - 1.
Original entry on oeis.org
1, 16, 6720, 16777216, 1148854468608, 2283836902459047936, 18326253047993428082688000, 5192296858534827628530496329220096, 37561472427665521549351504937293279395840000, 1720883444277066617294561853430153730874784623341076480
Offset: 1
Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003
-
\\ see Reiner reference.
F(u,r)={prod(i=1, r, (1-u^(-i)))}
a(n, q=4)={my(D=ffgen(q)); my(f=factor(D^0*(x^n-1))); q^(n^2-n)*F(q,n)/prod(i=1, #f~, F(q^poldegree(f[i,1]), f[i,2]))} \\ Andrew Howroyd, Jul 08 2018
A089036
Number of n X n matrices over GF(3) with characteristic polynomial x^n - 1.
Original entry on oeis.org
1, 12, 729, 758160, 2972290464, 354396766517640, 92079975413927255040, 939180873931369976460153600, 22528399544939174411840147874772641, 11276516942788127325350557035641264267894784, 25780902234356363794160964471948503247074139517747200
Offset: 1
Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003
-
\\ see Reiner reference.
F(u,r)={prod(i=1, r, (1-u^(-i)))}
a(n, q=3)={my(D=ffgen(q)); my(f=factor(D^0*(x^n-1))); q^(n^2-n)*F(q,n)/prod(i=1, #f~, F(q^poldegree(f[i,1]), f[i,2]))} \\ Andrew Howroyd, Jul 08 2018
Showing 1-3 of 3 results.