Details Page for 0.7311

Complete Solution is Known:

Period:  
Preperiod:  
Quotient Size:   1610
P-Portion Size:   205
Tame?   No

MSV File: q-0.7311.msv

Growth Pattern:

Heap   Q-Size   P-Size
121
262
5123
7163
10204
129616
1317623
1420229
1524435
1632644
1765482
1978297
2079097
211026141
221490192
231610205

(Click on a heap to see details)

Details for Q22(0.7311):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q | a2=1, b6=b4, bc2=b, c3=c, b2d=ab4, bd3=abd2, d4=ad3, be=b2, c2e=e, d3e=abd2, de2=ab4, e3=b5, b5f=b3f, bdf=ab3f, cdf=ab2cf, d2f=b4f, def=ab3f, e2f=b2f, b2f2=b4cf, c2f2=f2, df2=ab4cf, f3=cf2, b2g=ab4, c2g=g, bdg=b5, d2g=ab4, deg=b5, e2g=ab4, dfg=b4f, efg=acef2, eg2=bg2, bfg2=cef2, f2g2=cfg2, g3=ag2, b2h=b5, c2d2h=d2h, d3h=ad2h, eh=abdh, c2fh=fh, dfh=ab3f, gh=ab5, h2=b4, b2i=ab5, c2i=i, di=b5, e2i=ab5, ef2i=ab4cf, g2i=abg2, hi=ab4, i2=b4, b3j=b5, bdj=ab5, c2dj=dj, d2j=b4, dej=ab5, e2j=b4, bfj=b3f, c2fj=fj, dfj=ab4f, efj=b3f, bgj=ab5, egj=ab5, f2gj=cfgj, g2j=agj, hj=b5, ij=ab5, j2=b4, b3k=ab5, bdk=b5, c2d2k=d2k, d3k=ad2k, d2ek=ab5, e2k=b2k, efk=bfk, bf2k=ab3cf, bgk=b5, egk=b5, f2gk=cfgk, fg2k=afgk, bhk=ab4, c2hk=hk, dhk=ahk, fhk=ab3f, ik=b5, jk=ab4, k2=b4, b2l=b5, bd2l=b4, c2d2l=d2l, d2el=abdl, e2l=b5, bfl=b4f, cfl=ef2, efl=b4f, f2l=ef2, bgl=ab4, egl=ab4, fgl=acef2, g2l=agl, bhl=b5, c2hl=hl, dhl=ahl, fhl=b4f, eil=ab5, fil=ab4f, gil=b4, bjl=b4, c2jl=jl, djl=ab5, ejl=b4, fjl=b3f, d2kl=abd2, dekl=abkl, gkl=b5, hkl=abd2h, l2=b4, b2m=b4f, bd2m=b3f, c2d2m=d2m, e2m=b4f, ef2m=cef2, dg2m=adgm, fg2m=cfg2, c2hm=hm, fhm=f2h, efim=b2cfk, egim=ab2fk, bjm=b3f, c2jm=jm, djm=bdhm, ejm=b3f, fjm=f2j, gjm=fgj, bkm=ab3f, cdkm=b4cf, d2km=ab4f, ekm=ab3f, f2km=cf2k, gkm=fgk, hkm=ab3f, bdlm=b2fk, c2dlm=dlm, delm=ablm, flm=ef2, glm=acef2, ilm=ab4f, jlm=b3f, cklm=ab3cf, dklm=b3f, c2m2=m2, d2m2=b4cf, dem2=ab3cf, dfm2=ab4f, efm2=cef2, f2m2=cfm2, bgm2=abcg2m, dgm2=cdgm, egm2=abcg2m, fgm2=afg2, g2m2=agm2, im2=abcg2m, dkm2=b4cf, fkm2=cf2k, lm2=ef2, fm3=cfm2, gm3=cgm2, km3=cf2k, bm4=bcm3, em4=cem3, hm4=chm3, jm4=cjm3, m6=m4, b2n=abj, d2n=ad2h, den=bdn, e2n=aej, c2fn=fn, dfn=b3f, efn=bfn, egn=bgn, bfgn=abcf2n, f2gn=af2n, bg2n=abgn, dg2n=adgn, fg2n=cf2n, bhn=ab5, chn=ab2cj, dhn=b4, fhn=ab4f, bin=b5, ein=b5, f2in=abf2n, gin=abgn, jn=ab5, kn=ahk, bln=ab5, c2ln=ln, eln=ab5, fln=bcf2n, hln=ab5, iln=b5, c2mn=mn, dmn=d2hm, emn=bmn, fmn=f2n, g2mn=agmn, hmn=ab4f, imn=bgmn, gm2n=cgmn, m4n=cm3n, n2=b4, bo=ab2k, c2o=o, do=hk, eo=ab2k, f2o=b3cf, go=ab5, ho=b4, io=ab4, jo=b5, ko=ab5, lo=bd2h, mo=b3f, no=ab4, o2=b4, b2p=ab2j, c2p=p, bdp=b5, d3p=ad2p, ep=aej, dfp=b4f, bf2p=bcfp, bgp=b5, fg2p=acf2gp, hp=ab5, bfip=bcf2gi, f2ip=cfip, gip=ab5, jp=gj, bkp=b5, fkp=fgk, dg2kp=adgj, blp=ab4, dlp=b5, flp=ab3f, glp=alp, ilp=b4, klp=b5, bfmp=bcmp, f2mp=cfmp, fgmp=f2gp, bimp=bf2gim, fimp=cimp, kmp=fgk, lmp=ab3f, bm2p=ab3cf, fm2p=acf2gp, dm4p=dm2p, m5p=m3p, bnp=b4, dnp=ab5, fnp=b3f, gnp=anp, inp=ab4, lnp=b4, mnp=b3f, op=ab5, bp2=b5, f2p2=cfp2, fgp2=afp2, g2p2=agp2, ip2=ab5, gkp2=g2kp, lp2=alp, fmp2=cfp2, dgmp2=b4f, gm2p2=acfp2, m4p2=m2p2, np2=ab5, p3=ap2, bdq=ab3q, d3q=ad2q, deq=ab3q, bfq=bcf2m, c2fq=fq, dfq=ab4cf, efq=ef2, f2q=f2m, dgq=b4q, fgq=cf2gm, bg2q=aegq, c2hq=hq, dhq=ab5q, fhq=f2h, eiq=ab4q, fiq=cf2im, c2jq=jq, djq=ab2jq, fjq=f2j, bkq=ab5q, c2kq=kq, dkq=b4q, ekq=ab5q, g2kq=agkq, hkq=ab5q, c2lq=lq, d2lq=adlq, elq=b4q, flq=ef2, hlq=b4q, klq=ab5q, bmq=bcfm2, c2mq=mq, d2mq=admq, emq=ef2, gmq=acfg2, hmq=f2h, imq=aef2, jmq=f2j, fkmq=ckm2, lmq=ef2, dm2q=ab4f, fm2q=cfm2, km2q=cf2k, m4q=m2q, c2nq=nq, dnq=bjq, fnq=f2n, g2nq=agnq, hnq=ab2jq, inq=bgnq, lnq=abgnq, mnq=f2n, oq=b5q, fpq=fmp, g2pq=agpq, bipq=bgiq, kpq=gkq, dmpq=admq, dp2q=d2pq, b4q2=b4cf, c2q2=q2, d2q2=b4cf, fq2=fm2, gq2=acfg2, bhq2=bf2h, iq2=aef2, bjq2=abcfk, kq2=km2, blq2=ab2cfk, dlq2=ab3cf, jlq2=b3cf, mq2=fm2, bpq2=acfo, dpq2=ab2cfk, lpq2=ab3cf, npq2=b3cf, p2q2=cfp2, bq3=bfm2, dq3=b2fk, eq3=cef2, hq3=cf2h, jq3=cf2j, lq3=cef2, nq3=cf2n, pq3=acf2gp, q4=cfm2>

P = {a, b2, b4, ac, ac2, d2, c2d2, ad3, ac2d3, e2, acf, b2cf, b4cf, af2, g, cg, cfg, f2g, ag2, acg2, acfg2, ah, abch, dh, bcdh, abcd2h, bcfh, af2h, bi, ei, bf2i, bcfgi, b2j, acj, ac2j, acfj, gj, cgj, cfgj, ak, ab2k, dk, c2dk, ad2k, abcfk, af2k, adgk, dg2k, bl, abdl, el, adel, hl, ail, ackl, cekl, afkl, dfkl, acm, acdm, cd2m, acd3m, afm, ac2fm, adfm, acf2m, gm, cgm, fgm, cf2gm, ag2m, acg2m, achm, cdhm, bcim, ceim, bcf2im, bfgim, ac2fkm, ablm, aelm, ahlm, klm, am2, adm2, acfm2, gm2, cgm2, bhm2, abdhm2, ajm2, am3, acm3, achm3, cdhm3, am4, adm4, acm5, acdm5, an, ac2n, dn, abcdn, bcfn, af2n, bgn, in, cfin, ln, cln, acgln, abcmn, bcgmn, lmn, abm2n, acm3n, cp, acdp, cd2p, cfp, agp, acgp, acfgp, g2p, cg2p, adkp, d2kp, dgkp, acg2kp, mp, cmp, acd2mp, agmp, acgmp, g2mp, m2p, cm2p, agm2p, acgm2p, m3p, cm4p, p2, adp2, d2p2, cfp2, agp2, dgp2, ckp2, acdkp2, cd2kp2, amp2, dmp2, ad2mp2, m2p2, adm2p2, am3p2, q, abcq, ab3cq, ab5cq, adq, d2q, aceq, afq, bcgq, cegq, achq, ciq, acgiq, abcjq, acejq, afkq, lq, adlq, acjlq, amq, acfmq, kmq, acm2q, am3q, bcpq, acipq, clpq, cm2p2q, aq2, b2q2, adq2, e2q2, ahq2, anq2, aq3, acq3}

Phi = 1 a b ab a c b d b2 e f g h i j k l m b4 n o p q

Monoid Structure

Idempotent  |G|  |Arch|
122
b48416
c244
ad326
ac2d3412
b4cf *8774
f2410
g248
cfg2428
cfm2448
agm2412
m4822
p248
d2p2416
cfp2484
agp2412
m2p2828