Details Page for 0.7311

Complete Solution is Known:

MSV File: q-0.7311.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₂₃(0.7311):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r | 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, efl=b⁴f, f²l=cfl, bgl=ab⁴, egl=ab⁴, fgl=ac²fl, 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, cfkl=ab³cf, gkl=b⁵, hkl=abd²h, bl²=b⁵, c²l²=l², dl²=ab⁴, el²=b⁵, fl²=b⁴f, gl²=al², hl²=b⁵, il²=ab⁵, jl²=b⁴, kl²=ab⁴, l³=b⁵, 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=cfl, glm=ac²fl, ilm=ab⁴f, jlm=b³f, cklm=ab³cf, dklm=b³f, l²m=b⁴f, 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=cfl, 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, l²n=ab⁵, 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, glp=alp, ilp=b⁴, klp=b⁵, l²p=al², bfmp=bcmp, f²mp=cfmp, fgmp=f²gp, bimp=bf²gim, fimp=cimp, kmp=fgk, lmp=flp, 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=cfl, hlq=b⁴q, klq=ab⁵q, bmq=bcfm², c²mq=mq, d²mq=admq, emq=ef², gmq=acfg², hmq=f²h, imq=aef², jmq=f²j, fkmq=ckm², lmq=cfl, 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, l²q²=b⁴cf, mq²=fm², bpq²=acfo, dpq²=ab²cfk, lpq²=cflp, npq²=b³cf, p²q²=cfp², bq³=bfm², dq³=b²fk, eq³=cef², hq³=cf²h, jq³=cf²j, lq³=c²fl, nq³=cf²n, pq³=acf²gp, q⁴=cfm², br=b²j, c²r=r, d²r=ahk, er=b²j, dfr=ab³f, f²r=cfr, dgr=adgn, fgr=afr, g²r=agr, hr=b⁴, ir=ab⁴, jr=jl, kr=bil, flr=afgj, l²r=agjl, dmr=ab³f, fmr=cfr, lmr=afgj, gm²r=cgmr, m³r=cm²r, dnr=b⁴, fnr=bcf²n, gnr=bgn, lnr=ab⁵, mnr=bcm²n, or=b⁴, dpr=b⁵, mpr=fpr, npr=b⁴, fp²r=afpr, dqr=ab⁵q, fqr=cfr, lqr=agjq, mqr=cfr, nqr=abgnq, pq²r=cfpr, q³r=fr, dr²=ab⁴, fr²=b⁴f, gr²=ar², lr²=agjl, mr²=b⁴f, nr²=ab⁵, pr²=ar², q²r²=b⁴cf, r³=b⁵>

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, l², 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, alr, aclr, glr, cglr, anr, lpr, cqr, acgqr, acpqr, cgpqr, cp²qr, r²}

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

Monoid Structure