Details Page for 0.1524

Complete Solution is Known:

MSV File: q-0.1524.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₂₃(0.1524):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p | a²=1, b⁴=b², b²c²=b², bc⁴=bc², c⁵=c³, b²d=ab², bcd=abc³, c⁴d=c²d, c³d²=cd², d³=ad², be=abd², c²e=c²d, cde=cd², d²e=ade, e²=d², b²f=b³c, bcf=b², c³f=bc², bdf=abf, cdf=abc², cef=abc², def=d²f, bf²=b³, cf²=b²c, d²f²=b², ef²=ab², f⁴=f², b²g=ab³, cdg=ac³g, bd²g=abdg, ceg=ac³g, deg=aeg, cfg=bc²g, d²fg=adfg, efg=dfg, f²g=ab³, bc²g²=b³, c⁴g²=c²g², bdg²=ab³, eg²=ad²g², bfg²=b²c, dfg²=bfg, bg³=ab², cg³=abcg², d²g³=ab³, fg³=ab²c, g⁴=b², b²h=ab³, bch=ab²c, c²h=abc², bdh=b², d²h=abd², eh=bd², bfh=ab³c, dfh=bf, f²h=ab³, fgh=abfg, bg²h=cfh, cg²h=ab³c, g³h=acfh, cdh²=ab²c, cfh²=dg²h, cgh²=ab³c, dgh²=bgh, bh³=dh², g²h³=g²h, ch⁴=ch², dh⁴=dh², fh⁴=fh², h⁵=h³, b²i=b²c, bd²i=bc²i, cd²i=ac³di, ei=ad²i, bfi=b², c²fi=bci, d²fi=adfi, f²i=b²c, c³gi=cgi, bdgi=abc²gi, d²gi=c²gi, fgi=bcgi, bg²i=bcg², dg³i=bcg², bhi=ab²c, fhi=cfh, ghi=abc²gi, h²i=ch², bi²=b³, c²i²=i², di²=ai², fi²=b³c, gi²=abc³i, hi²=ab³, i³=b²c, bj=bc³, c³j=c²d², dj=ac²j, ej=ac²j, cfj=bc³, f²j=b²c, cgj=c²g, fgj=bc²g, g²j=c³g², chj=abc², gh²j=ab³c, fh³j=fhj, h⁴j=h²j, cij=ac²di, fij=bc²i, gij=cgi, i²j=ci², cj²=c²j, fj²=bc³, gj²=c⁴g, hj²=abc², ij²=ac²di, j³=cd², bk=abc³, c²k=c³d, dk=cd², ek=cd², fk=abc², cg²k=ac²g², g³k=b³c, cghk=bc²g, g²hk=b³c, h²k=fh³, cik=c²di, g²ik=acg²i, i²k=aci², cjk=acd², gjk=ac⁴g, hjk=fj, ijk=c²di, j²k=acd², k²=c²d², b²l=ab³c, cl=abc², bdl=abl, del=ael, efl=ad²fl, d²gl=adgl, dfgl=afgl, bg²l=ab²c, dg²l=bgl, fg²l=abfgl, g³l=b²c, bhl=b³c, dhl=bl, ghl=abgl, h²l=h³j, bil=ab², dil=bc³i, fil=ab²c, gil=abcgi, hil=b², i²l=ab³c, jl=abc², kl=fj, l²=af³l, b²m=b³c, bc²m=b²c, c³m=bc², c²dm=abc³, bd²m=b²c, cd²m=bc², cem=abc², dem=d²m, bfm=b³, efm=dfm, f²m=b³c, bdgm=b³c, egm=ad²gm, fgm=bcgm, c²g²m=b³c, d²g²m=b³c, bhm=ab³c, fhm=ab³, ghm=b³c, h²m=fh², cim=bc²i, bdim=ac²fm, d²im=bc³i, fim=b²c, bgim=bcgm, dg²im=bcgm, dhim=c²fm, i²m=b³c, c²jm=bc², fjm=b²c, hjm=fhj, ijm=bc²i, j²m=bc³, cgkm=aghk, g²km=ab³, hkm=cdhm, ikm=abc²i, jkm=abc³, blm=ab³, d²lm=ad²fm, elm=d²fm, flm=ab³c, glm=abcgm, hlm=fh²j, ilm=ab²c, m²=b², bn=b²c, cn=bc², en=ad²n, d²fn=b², gn=bcg, hn=ab²c, in=adfi, jn=bc², kn=abc², dln=adfn, fln=af²n, dmn=ad²fm, fmn=b³c, lmn=ab³c, n²=b², f²o=b²o, cdho=c²fo, ghjo=cgho, d²lo=adlo, ilo=abc³io, d²fmo=bfglo, himo=chmo, dlmo=bfglo, d²no=adno, fno=b²o, lno=ab²o, b²o²=b², bc²o²=bc², ceo²=c³do², efo²=dfo², c³go²=c³g, c²g²o²=c²g², cfho²=fhj, cgho²=ghj, dg²ho²=fh²j, ch²o²=h²j, c²dio²=c²di, d²io²=d²i, dfio²=dfi, cgio²=cgi, i²o²=i², fjo²=fj, hjo²=hj, chko²=fj, bfglo²=d²fm, d²mo²=d²m, dno²=ad²n, bd²o³=bd²o, bfo³=bfo, d²fo³=d²fo, bcgo³=bcgo, bdgo³=bdgo, fgo³=fgo, cg²o³=cg²o, d²g²o³=d²g²o, dg³o³=dg³o, bgio³=bgio, dgio³=dgio, g²io³=g²io, cgko³=ac⁴go, g²ko³=ac³g²o, ghko³=bc³go, blo³=blo, flo³=flo, g²lo³=g²lo, hlo³=hlo, bgmo³=bgmo, dgmo³=dgmo, g²mo³=g²mo, kmo³=cdmo³, no³=no, c³o⁴=c³, c²do⁴=c²d, cd²o⁴=cd², c²fo⁴=c²f, bgo⁴=bgo², c²go⁴=c²g, dgo⁴=dgo², ego⁴=ego², g³o⁴=g³o², bho⁴=bho², fho⁴=fho², dh²o⁴=dh²o², bcio⁴=bci, c²io⁴=c²i, bdio⁴=bdi, cfio⁴=cfi, gjo⁴=gj, ijo⁴=ijo², gko⁴=ac³g, hiko⁴=hiko², jko⁴=jk, dlo⁴=dlo², elo⁴=elo², glo⁴=glo², c²mo⁴=c²m, bdmo⁴=bdm, emo⁴=em, cfmo⁴=cfm, dfmo⁴=dfm, jmo⁴=jm, bdo⁵=bdo, cdo⁵=cdo, dfo⁵=efo, g²o⁵=g²o³, gho⁵=gho³, h²o⁵=h²o³, bio⁵=bio, dio⁵=dio, chio⁵=chio, bmo⁵=bmo, dmo⁵=dmo, fmo⁵=fmo, gimo⁵=gimo, lmo⁵=lmo, bo⁶=bo², c²o⁶=c²o², do⁶=do², eo⁶=eo², fo⁶=fo², cho⁶=cho², cio⁶=cio², hio⁶=hio², jo⁶=jo², iko⁶=iko⁴, lo⁶=lo², hmo⁶=hmo², imo⁶=imo², co⁷=co³, ho⁷=ho³, mo⁷=mo³, o⁸=o⁴, b²p=ab³, bc²p=bcgi, bdp=abcgi, dep=d²p, bfp=ab³c, efp=dfp, f²p=ab³, bgp=abcgm, cgp=ac²gm, dgp=abdg, egp=abdg, fgp=abfg, g²p=acg²m, fhp=b³c, ghp=abhp, bh²p=abcg²mo², ch²p=ab³c, dh²p=b³, h³p=afhj, bip=acfm, cfip=acfm, dfip=d²fm, gip=abc²gi, cdhip=acdhm, i²p=ab³, fjp=bcgi, gjp=ac²gm, h²jp=ab³c, hijp=bcg²mo², ckp=c²dp, gkp=ghk, hkp=bc²gi, ikp=c³dip, jkp=ac²d²p, blp=b³c, d²lp=adlp, elp=dlp, flp=abfl, glp=abgl, hlp=ab³c, bmp=ab³c, cmp=bcgi, dmp=abc²gi, emp=abc²gi, fmp=ab³, gmp=b³c, hmp=b³c, imp=ab², jmp=bcgi, lmp=b³, dnp=anp, fnp=ab³, lnp=b³, mnp=ab³, dhop=cfop, c²fo²p=bco²p, bho²p=bhp, h²o²p=h²p, dlo²p=alo²p, no²p=np, ko³p=c³do³p, lo³p=adlop, mo³p=bc²gio, bco⁴p=c²fp, cfo⁴p=cfp, fio⁴p=fip, d²o⁵p=d²op, ho⁵p=hop, co⁶p=co²p, io⁶p=io²p, o⁷p=o³p, bp²=b³, c³p²=cp², c²dp²=dp², d²p²=abc²g, ep²=dp², fp²=b³c, gp²=ab³, hp²=ab³, c²ip²=ip², dip²=bc²gi, jp²=abc³g, lp²=ab³c, mp²=b³c, np²=b³c, kop²=cdop², co⁴p²=cp², do⁴p²=dp², io⁴p²=ip², o⁵p²=op², p³=ab³>

P = {a, b², c², c⁴, ac²d, d², c²d², ae, de, df, f², df³, ag, abcg, abc³g, dfg, cg², c³g², ah, acfh, cgh, ah², agh², ah³, agh³, ah⁴, agh⁴, ci, c³i, acdi, ac³di, ag²i, ac²g²i, dg²i, i², aj, ahj, ah³j, ij, j², ack, ag²k, aik, al, ad²l, el, dfl, af³l, df³l, bfgl, bm, ac²m, ad²m, adfm, ac²gm, bcg²m, cdhm, abim, gim, ag³im, him, gkm, dlm, an, adfn, af³n, aln, afo, ad²fo, efo, dgo, ad²go, ego, abgho, g²ho, abh²o, gh²o, adh³o, gh⁴o, cgio, afh²jo, agko, ahko, aglo, dglo, eglo, afhlo, mo, gmo, adgmo, d²gmo, o², c²o², c⁴o², ado², ac²do², d²o², c²d²o², aeo², deo², abcgo², afgo², dfgo², cg²o², acho², ag²ho², h²o², ag²h²o², h⁴o², cio², c³io², acdio², ag²io², dg²io², ahio², cjo², ijo², j²o², alo², dlo², elo², fglo², amo², bcmo², dmo², emo², c²fmo², acgmo², bg²mo², ag³mo², bimo², g³imo², agjmo², gkmo², lmo², afo³, dfo³, ago³, dgo³, ad²go³, ego³, abg²o³, g³o³, abgho³, g²ho³, abh²o³, gh²o³, adh³o³, gh⁴o³, agko³, ahko³, glo³, adglo³, eglo³, acmo³, aimo³, ajmo³, o⁴, c²o⁴, ado⁴, d²o⁴, aeo⁴, deo⁴, acho⁴, h²o⁴, ag²h²o⁴, h⁴o⁴, cio⁴, acdio⁴, ahio⁴, cjo⁴, j²o⁴, alo⁴, bmo⁴, chmo⁴, abimo⁴, gimo⁴, afo⁵, ago⁵, ahko⁵, mo⁵, aimo⁵, o⁶, amo⁶, acgmo⁶, ago⁷, ap, abcp, ac²fp, ad²fp, chp, ah²p, hjp, lp, kmp, anp, bcop, c³op, dop, ac³dop, cd²op, fop, abhop, h²op, aciop, c²jop, alop, afo²p, dfo²p, ad²fo²p, cho²p, kmo²p, o³p, ac²o³p, ac⁴o³p, c²do³p, ac²d²o³p, cio³p, acjo³p, ijo³p, aj²o³p, afo⁴p, co⁵p, acjo⁵p, aj²o⁵p, cp², acdp², o²p², ac²o²p², cio²p²}

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

Monoid Structure