Details Page for 0.3026

Complete Solution is Known:

Period:  
Preperiod:  
Quotient Size:   5436
P-Portion Size:   617
Tame?   No

MSV File: q-0.3026.msv

Growth Pattern:

Heap   Q-Size   P-Size
121
562
15123
16245
19487
2012015
2334446
261364162
275436617

(Click on a heap to see details)

Details for Q27(0.3026):

Q = <a,b,c,d,e,f,g,h,i,j,k | a2=1, b4=b2, b2c=ab3, c2=1, bd2=b, d3=d, b3e=be, bce=ab2e, d2e3=e3, b2e4=e4, ce4=abe4, e5=ae4, b3f=bf, bcf=ab2f, d2f=f, b2ef=ef, cef=abef, b2f2=f2, cf2=abf2, e4f3=ae3f3, e3f4=ae4f2, f6=f4, bg=bc, e3g=abe3, fg=cf, de2g2=b2de2, g3=cg2, de2gh=abde2h, g2h=cgh, b2de2h2=de2h2, cde2h2=abde2h2, d2e2h2=b2e2h2, e3h2=b2e3, gh2=ch2, h3=cgh, bi=bd, d2i=i, e4i=de4, fi=df, g2i=dg2, ghi=dgh, h2i=dh2, i2=d2g2, b3j=bj, bcj=ab2j, e4j=ade4, b2fj=fj, cfj=abfj, e3f3j=ade3f3, deg2j=b2dej, deghj=abdehj, b2deh2j=deh2j, cdeh2j=abdeh2j, d2eh2j=b2eh2j, e2j2=b2e2, f3j2=f3, dg2j2=b2dj2, dghj2=abdhj2, b2dh2j2=dh2j2, cdh2j2=abdh2j2, d2h2j2=b2h2j2, ej3=b2ej, j4=b2j2, b3k=bk, bck=ab2k, d2e2k=e2k, e4k=e4, b2fk=fk, cfk=abfk, e3f2k=ae4f2, degk=abdek, e2gk=abe2k, g2k=cgk, b2deh2k=deh2k, cdeh2k=abdeh2k, d2eh2k=b2eh2k, b2e2h2k=e2h2k, ce2h2k=abe2h2k, gik=dgk, dgjk=abdjk, b2dh2jk=dh2jk, cdh2jk=abdh2jk, d2h2jk=b2h2jk, b2dj2k=dj2k, cdj2k=abdj2k, d2j2k=b2j2k, b2ej2k=ej2k, cej2k=abej2k, gj2k=cj2k, ij2k=dj2k, b2j3k=j3k, cj3k=abj3k, d2ek2=ek2, e3k2=e3k, f3k2=f5, dgk2=abdk2, egk2=abek2, b2dh2k2=dh2k2, cdh2k2=abdh2k2, d2h2k2=b2h2k2, b2eh2k2=eh2k2, ceh2k2=abeh2k2, b2j2k2=j2k2, cj2k2=abj2k2, j3k2=b2jk2, d2k3=k3, gk3=abk3, b2h2k3=h2k3, ch2k3=abh2k3, j2k3=b2k3, e2k4=e2k2, k5=k3>

P = {a, b2, c, ad, cd, ad2, cd2, be, e2, b2e2, d2e2, ae3, ab2e3, e4, abf, aef, abe2f, be3f, abe4f, f2, bef2, e2f2, ae3f2, e4f2, af3, abef3, bde2f3, abde3f3, f4, bef4, e2f4, af5, abef5, bde2f5, g, acg, dg, acdg, d2g, acd2g, ce2g, cd2e2g, ag2, cg2, adg2, cdg2, ad2g2, cd2g2, e2g2, ah, ch, adh, b2dh, cdh, ad2h, cd2h, bdeh, ace2h, de2h, b2de2h, abe3h, ce3h, be4h, abdfh, adefh, abde2fh, e3fh, ae4fh, df2h, bdef2h, de2f2h, abe3f2h, be4f2h, adf3h, abdef3h, be2f3h, e3f3h, df4h, bdef4h, de2f4h, adf5h, abdef5h, be2f5h, gh, acgh, dgh, acdgh, d2gh, acd2gh, ae2gh, ah2, b2h2, ch2, adh2, cdh2, ad2h2, cd2h2, beh2, e2h2, b2e2h2, abfh2, aefh2, abe2fh2, f2h2, bef2h2, e2f2h2, af3h2, abef3h2, bde2f3h2, f4h2, bef4h2, e2f4h2, af5h2, abef5h2, bde2f5h2, ai, ci, adi, cdi, de2i, ade3i, gi, acgi, dgi, acdgi, cde2gi, ahi, chi, adhi, cdhi, e2hi, cde3hi, bj, ej, b2ej, d2ej, be2j, ade2j, de3j, b2de3j, afj, abefj, ae2fj, abde3fj, bf2j, ef2j, be2f2j, de3f2j, abf3j, aef3j, abe2f3j, bf4j, ef4j, ade2f4j, abf5j, aef5j, abe2f5j, cegj, cd2egj, eg2j, bdhj, acehj, dehj, b2dehj, bde2hj, acde3hj, adfhj, abdefhj, ade2fhj, bdf2hj, def2hj, bde2f2hj, abdf3hj, adef3hj, abde2f3hj, bdf4hj, def4hj, ae2f4hj, abdf5hj, adef5hj, abde2f5hj, aeghj, bh2j, eh2j, b2eh2j, be2h2j, afh2j, abefh2j, ae2fh2j, bf2h2j, ef2h2j, be2f2h2j, abf3h2j, aef3h2j, abe2f3h2j, bf4h2j, ef4h2j, ade2f4h2j, abf5h2j, aef5h2j, abe2f5h2j, deij, ae2ij, e3ij, cdegij, ehij, ace3hij, j2, b2j2, d2j2, bej2, adej2, abfj2, aefj2, f2j2, bef2j2, cgj2, cd2gj2, g2j2, achj2, dhj2, b2dhj2, bdehj2, abdfhj2, adefhj2, df2hj2, bdef2hj2, aghj2, h2j2, b2h2j2, beh2j2, abfh2j2, aefh2j2, f2h2j2, bef2h2j2, dij2, aeij2, cdgij2, hij2, bj3, adj3, afj3, bf2j3, bdhj3, adfhj3, bdf2hj3, bh2j3, afh2j3, bf2h2j3, aij3, abk, aek, ab2ek, ad2ek, e2k, b2e2k, ae3k, ab2e3k, fk, befk, abe2fk, be3fk, af2k, e2f2k, f3k, bef3k, af4k, abef4k, f5k, bef5k, ade2f5k, acegk, abdhk, cehk, adehk, ab2dehk, de2hk, b2de2hk, abe3hk, ce3hk, dfhk, bdefhk, abde2fhk, e3fhk, abf2hk, aef2hk, de2f2hk, df3hk, bdef3hk, adf4hk, abdef4hk, df5hk, bdef5hk, ae2f5hk, eghk, abh2k, aeh2k, ab2eh2k, e2h2k, fh2k, befh2k, abe2fh2k, abdf2h2k, adef2h2k, e2f2h2k, f3h2k, bef3h2k, af4h2k, abef4h2k, f5h2k, bef5h2k, ade2f5h2k, adeik, de2ik, ade3ik, aehik, e2hik, cde3hik, ajk, ab2jk, ad2jk, abejk, cd2ejk, be2jk, ace2jk, de3jk, b2de3jk, bfjk, efjk, ae2fjk, abde3fjk, abef2jk, bf3jk, ef3jk, abf4jk, aef4jk, bde2f4jk, bf5jk, ef5jk, acgjk, chjk, adhjk, ab2dhjk, abdehjk, cdehjk, bde2hjk, acde3hjk, bdfhjk, defhjk, ade2fhjk, af2hjk, abdef2hjk, bdf3hjk, def3hjk, abdf4hjk, adef4hjk, e2f4hjk, bdf5hjk, def5hjk, ghjk, ah2jk, ab2h2jk, abeh2jk, be2h2jk, bfh2jk, efh2jk, ae2fh2jk, adf2h2jk, abef2h2jk, bf3h2jk, ef3h2jk, abf4h2jk, aef4h2jk, bf5h2jk, ef5h2jk, adijk, cdeijk, acde2ijk, e3ijk, ahijk, cehijk, ace3hijk, abj2k, aej2k, fj2k, befj2k, abf2j2k, aef2j2k, abdhj2k, adehj2k, dfhj2k, bdefhj2k, abdf2hj2k, adef2hj2k, abh2j2k, aeh2j2k, fh2j2k, befh2j2k, abf2h2j2k, aef2h2j2k, aj3k, bfj3k, af2j3k, adhj3k, bdfhj3k, adf2hj3k, ah2j3k, bfh2j3k, af2h2j3k, k2, b2k2, d2k2, aek2, ab2ek2, e2k2, b2e2k2, abfk2, befk2, abe2fk2, f2k2, adef2k2, e2f2k2, cgk2, achk2, dhk2, b2dhk2, adehk2, ab2dehk2, de2hk2, b2de2hk2, abdfhk2, bdefhk2, abde2fhk2, df2hk2, aef2hk2, de2f2hk2, aghk2, h2k2, b2h2k2, aeh2k2, e2h2k2, abfh2k2, befh2k2, abe2fh2k2, f2h2k2, adef2h2k2, e2f2h2k2, dik2, adeik2, de2ik2, hik2, aehik2, e2hik2, bjk2, acd2jk2, abejk2, cejk2, be2jk2, ace2jk2, afjk2, efjk2, ae2fjk2, bf2jk2, be2f2jk2, bdhjk2, acdhjk2, abdehjk2, cdehjk2, bde2hjk2, adfhjk2, defhjk2, ade2fhjk2, bdf2hjk2, bh2jk2, abeh2jk2, be2h2jk2, afh2jk2, efh2jk2, ae2fh2jk2, bf2h2jk2, be2f2h2jk2, acdijk2, cdeijk2, acde2ijk2, achijk2, cehijk2, j2k2, aej2k2, abfj2k2, befj2k2, f2j2k2, dhj2k2, adehj2k2, abdfhj2k2, bdefhj2k2, df2hj2k2, h2j2k2, aeh2j2k2, abfh2j2k2, befh2j2k2, f2h2j2k2, k3, b2k3, aek3, ab2ek3, e2k3, b2e2k3, abfk3, befk3, abe2fk3, def2k3, dhk3, b2dhk3, adehk3, ab2dehk3, de2hk3, b2de2hk3, abdfhk3, bdefhk3, abde2fhk3, ef2hk3, h2k3, aeh2k3, e2h2k3, abfh2k3, befh2k3, abe2fh2k3, def2h2k3, dik3, adeik3, de2ik3, hik3, aehik3, e2hik3, bjk3, acjk3, abejk3, cejk3, be2jk3, ace2jk3, afjk3, efjk3, ae2fjk3, bdef2jk3, bdhjk3, acdhjk3, abdehjk3, cdehjk3, bde2hjk3, adfhjk3, defhjk3, ade2fhjk3, bef2hjk3, abe2f2hjk3, bh2jk3, abeh2jk3, be2h2jk3, afh2jk3, efh2jk3, ae2fh2jk3, bdef2h2jk3, acdijk3, cdeijk3, acde2ijk3, achijk3, cehijk3, k4, b2k4, aek4, ab2ek4, abfk4, befk4, f2k4, adef2k4, dhk4, b2dhk4, adehk4, ab2dehk4, abdfhk4, bdefhk4, df2hk4, aef2hk4, h2k4, aeh2k4, abfh2k4, befh2k4, f2h2k4, adef2h2k4, dik4, adeik4, hik4, aehik4, bjk4, acjk4, abejk4, cejk4, afjk4, efjk4, bf2jk4, abdef2jk4, bdhjk4, acdhjk4, abdehjk4, cdehjk4, adfhjk4, defhjk4, bdf2hjk4, bh2jk4, abeh2jk4, afh2jk4, efh2jk4, bf2h2jk4, abdef2h2jk4, acdijk4, cdeijk4, achijk4, cehijk4}

Phi = 1 a 1 a 1 b ab b a 1 a 1 b ab b c cdg adg2 d e f b g h adg2 i j k

Monoid Structure

Idempotent  |G|  |Arch|
144
b2816
d288
e4161584
e4f2 *321728
f464344
g248
d2g2832
h2812
b2h21632
d2h21632
f4h2128688
b2j216164
b2h2j232148
k41640
b2k432220
h2k464376