Details Page for 0.5247

Complete Solution is Known:

MSV File: q-0.5247.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₆(0.5247):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m | a²=1, b⁴=b², b²c²=b², bc⁴=bc², c⁵=c³, b²d=b³c, bcd=b², c²d=bc³, cd³=b³, bd⁴=b³, d⁶=d⁴, b²e=ab², bce=abc, c²e=ac², cde=acd, ce²=ace, bd²e²=b³, d³e²=b³c, e³=ae², b²f=ab², bc²f=abc², cdf=abc², bd³f=ab²c, d⁵f=d³f, bdef=b²c, d⁴ef=d²ef, be²f=abef, de²f=bcf, bf²=bc², cf²=c³, d²f²=b², def²=abc³, e²f²=aef², f³=c⁴f, b²g=ab³, bd³g=ab³c, d⁴g=ab³, ceg=acg, bd²eg=b², d³eg=b²c, e²g=aeg, c³fg=ac³g, d³fg=b²c, defg=abcfg, ef²g=c²fg, bg²=b³, cg²=b²c, d²g²=b², eg²=ag², fg²=ab², g³=ab³, bh=b², ch=abcf, d³h=abd³e, d²eh=ab³, e²h=aeh, dfh=d³g, efh=bc², f²h=bc², d²gh=abd²fg, fgh=abc²g, g²h=b³, h²=b², b²i=ab²c, bci=abc², c⁴i=c²i, d⁴i=ab²c, cei=aci, bd²ei=bdfg, d³ei=d²fg, bdfi=bd²fg, d²fi=b²c, befi=abc³, defi=abc², e²fi=aefi, f²i=c²i, c²gi=ac³g, bdgi=b³, d²gi=bdfg, begi=abgi, bfgi=bc³g, dfgi=bc²g, efgi=afgi, g²i=ab²c, ehi=acdi, ghi=cdgi, bd²i²=b³, d³i²=b³c, bei²=abi², bfi²=abc², dfi²=abc³, efi²=afi², egi²=agi², hi²=cdi², ei³=ai³, c²fi³=ac²i³, bi⁴=bi², c²i⁴=ac³i³, di⁴=de²i², gi⁴=gi², i⁵=i³, bj=abc, c²j=c³f, dj=acd, ej=aj, f²j=c³f, cgj=ac²g, g²j=ab²c, hj=bcf, cij=c²fi, fgij=acfgi, gi²j=acgi², j²=cfj, b²k=ab³c, bc³k=bck, bd²k=ab²c, d⁴k=ab³c, bdek=abdk, d³ek=bd²fg, be²k=abek, bcfk=abck, c⁴fk=c²fk, bdfk=b³, d²fk=b³c, befk=bc²k, defk=bck, e²fk=aefk, ef²k=ac⁴k, bcgk=b³, c³gk=abck, d³gk=b³, begk=abgk, degk=adgk, bfgk=ab³c, cfgk=bck, dfgk=ab³, f²gk=abc²k, dg²k=abdgk, hk=cdk, bdik=b³c, cdik=bik, d²ik=b³, eik=aik, bfik=bck, dfik=bc²k, bgik=ab³, dgik=ab³c, fgik=abck, cfjk=c⁴k, fgjk=abck, gijk=acgik, i³jk=aci³k, bk²=b³, c²k²=b², dk²=b³c, ek²=ak², fk²=ab², gk²=ab³, ik²=ad²gk, cjk²=ab², k³=ab³c, b²l=b³c, bcl=abck, bdl=b³, cdl=abi²k, d³l=b², bel=abl, de²l=adel, bfl=ac²gk, dfl=adfk, e²fl=aefl, ef²l=ac⁴l, gl=abl, hl=abi²k, bil=abi³k, d²il=ab³, eil=ail, di³l=dil, bkl=ab³, c⁴kl=c²kl, e²kl=aekl, f²kl=c²kl, dikl=b³, cjkl=c²fkl, k²l=b³c, l²=b², d⁴m=b²m, bdfm=bd³em, d²fm=ab²m, defm=abcfm, e²fm=aefm, bd²gm=ab²m, d³gm=ab²cm, begm=abgm, d²egm=ad²gm, f²gm=ac²fgm, d²hm=abd²em, fhm=abc²m, eghm=aghm, bd²im=ab³cm, d³im=ab³m, deim=adim, e²im=aeim, bfim=df²m, dfim=bc²m, egim=agim, him=cdim, ei²m=ai²m, d³km=ab²m, e²km=aekm, dfkm=abckm, f²km=c⁴km, e²lm=aelm, f²lm=c⁴lm, deklm=cdgkm, b²m²=b², bc³m²=bcm², c⁴m²=c²m², bd²m²=b³, d³m²=b³c, bem²=abm², e²m²=aem², bfm²=abc²m², dfm²=abcm², f²m²=c²m², egm²=agm², c²fgm²=ac²gm², ehm²=ahm², eim²=aim², cjm²=c²fm², gjm²=acgm², c²gkm²=abc²km², fgkm²=bc²km², jk²m²=ack²m², blm²=abi²km², d²elm²=cd²gm², cem³=acm³, bcgm³=ab²cm, dghm³=ab³cm, bckm³=ab²m, cdkm³=ab²cm, d²km³=ab³cm, ekm³=akm³, g²km³=abgkm³, bikm³=b²m, dilm³=ab²cm, dklm³=ab³cm, bcm⁴=b³c, em⁴=am⁴, c²fm⁴=ac²m⁴, c²gm⁴=ab³, d²gm⁴=ab³, fgm⁴=b³, dg²m⁴=ad²el, hm⁴=cdm⁴, c²im⁴=ac³m⁴, cd²im⁴=cdgm⁴, bdi³m⁴=bgi²m⁴, bgi³m⁴=bdi²m⁴, cgi³m⁴=cgim⁴, dgi³m⁴=dgim⁴, cfi⁴m⁴=cfi²m⁴, jm⁴=acm⁴, cfkm⁴=ac³km⁴, cgkm⁴=acdgm⁴, bdgkm⁴=d²ekl, dikm⁴=bdi²m⁴, gikm⁴=adgim⁴, ci³km⁴=cikm⁴, k²m⁴=b², c³lm⁴=clm⁴, dlm⁴=b², cflm⁴=aclm⁴, cilm⁴=ac²lm⁴, cklm⁴=bc²km², cd²m⁵=acgikm³, bdgm⁵=dghm, cdgm⁵=acgi²km³, bgi²m⁵=bdim⁵, cgi²m⁵=cgm⁵, di³m⁵=dim⁵, cfi³m⁵=cfim⁵, fi⁴m⁵=fi²m⁵, c²km⁵=ab³cm, bdkm⁵=cd²km, ci²km⁵=ckm⁵, i⁴km⁵=i²km⁵, clm⁵=bc²m³, i⁴lm⁵=i²lm⁵, fklm⁵=aghm³, c²m⁶=b², d²m⁶=d²i²m⁴, cfm⁶=acdgim⁴, cgm⁶=cgi²m⁴, bdi²m⁶=bgim⁶, cdi²m⁶=cdm⁶, bi³m⁶=bim⁶, fi³m⁶=fim⁶, gi³m⁶=gim⁶, i⁴m⁶=i²m⁶, i³km⁶=ikm⁶, i³lm⁶=ilm⁶, bdm⁷=ck²m³, cdm⁷=cdi²m⁵, bgm⁷=ab²m, g²m⁷=adelm³, bim⁷=ab³cm, dgim⁷=d²i²m⁵, fi²m⁷=fm⁷, i³m⁷=im⁷, bkm⁷=ab²cm, ckm⁷=ckm⁵, dkm⁷=ab²m, gkm⁷=ad²im⁵, i²km⁷=km⁷, i²lm⁷=lm⁷, bm⁸=b³, cm⁸=ci²m⁶, fm⁸=fi²m⁶, dgm⁸=d²i³m⁴, i²m⁸=m⁸, lm⁸=i²lm⁶, km⁹=km⁷, m¹⁰=m⁸>

P = {a, b², c², c⁴, d², d⁴, de, d³e, d⁵e, e², d²e², af, ac²f, ac⁴f, ad²f, ad⁴f, ae²f, f², aef², ag, abcg, abc³g, ad²g, deg, fg, bcfg, d²fg, g², bi, ac³i, cdi, bd²i, abei, be²i, c³fi, hi, d²hi, i², c²i², d²i², aei², e²i², d²e²i², afi², ac²fi², adgi², bi³, ac³i³, cdi³, i⁴, afi⁴, acj, cfj, adk, ad³k, dfk, adf²k, abgk, acdgk, cik, bi³k, aijk, k², dl, el, ackl, c³kl, ad²kl, cekl, d²ekl, cfkl, c³fkl, acefkl, afikl, ac²fikl, aci²kl, ac³i²kl, cfi²kl, c³fi²kl, c²i³kl, afi³kl, aci⁴kl, cfi⁴kl, jkl, fjkl, i²jkl, afi²jkl, cm, bc³m, bdm, bd³m, acem, abdem, abd³em, bde²m, acfm, cefm, bcgm, ac⁴gm, acd²gm, abcfgm, dg²m, acdim, abgim, acfgim, ai²m, dgi²m, ci³m, abgi³m, acdgi³m, ai⁴m, ajm, fjm, agijm, ai³jm, bkm, abekm, bfkm, c²gkm, aefgkm, cikm, gi²km, di³km, acgi³km, ajk²m, c²lm, c²flm, acilm, i²lm, fi²lm, aci³lm, cfi³lm, i⁴lm, afi⁴lm, cjlm, cfjlm, i³jlm, fi³jlm, ac³klm, ac³fklm, c²iklm, c²fiklm, ac³fi²klm, ac²i³klm, m², c²m², d²m², aem², ad²em², afm², ac²fm², efm², abcgm², g²m², bim², ac³im², cdim², c³fim², i²m², c²i²m², d²i²m², afi²m², ac²fi²m², adgi²m², bi³m², ac³i³m², cdi³m², i⁴m², afi⁴m², adkm², dekm², abgkm², acdgkm², cikm², bi³km², aijkm², k²m², dlm², adelm², klm², c³klm², ad²klm², fklm², c³fklm², acefklm², afiklm², ac²fiklm², aci²klm², ac³i²klm², cfi²klm², c³fi²klm², c²i³klm², afi³klm², aci⁴klm², cfi⁴klm², fjklm², i²jklm², afi²jklm², am³, bcm³, em³, ac²gm³, dgm³, acd²gm³, abim³, acdim³, cgim³, acfgim³, ai²m³, dgi²m³, ci³m³, abgi³m³, acdgi³m³, ai⁴m³, ai³jm³, adikm³, gi²km³, di³km³, acgi³km³, ck²m³, aelm³, eflm³, i²lm³, fi²lm³, aci³lm³, cfi³lm³, i⁴lm³, afi⁴lm³, i³jlm³, fi³jlm³, acklm³, ac³klm³, acfklm³, ac³fklm³, c²iklm³, c²fiklm³, ac³fi²klm³, ac²i³klm³, ajklm³, afjklm³, m⁴, c²m⁴, d²m⁴, afm⁴, abgm⁴, acdgm⁴, g²m⁴, acim⁴, abdim⁴, cfim⁴, i²m⁴, d²i²m⁴, afi²m⁴, bi³m⁴, cdi³m⁴, i⁴m⁴, afi⁴m⁴, ai²klm⁴, fi²klm⁴, ai⁴klm⁴, dm⁵, gim⁵, ci²m⁵, bdi²m⁵, acfi²m⁵, adgi²m⁵, ai⁴m⁵, lm⁵, aflm⁵, m⁶, afm⁶, abgm⁶, g²m⁶, i²m⁶, afi²m⁶, aci³m⁶, dgkm⁶, aklm⁶, ai²klm⁶, cm⁷, gim⁷, di²m⁷, m⁸, agm⁹, adim⁹}

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

Monoid Structure