Details Page for 0.3501

Complete Solution is Known:

MSV File: q-0.3501.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₈(0.3501):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q | a²=1, b³=b, b²c=c, c⁴=c³, b²d=d, c³d=c²d, cd²=d², d³=ad², b²e=e, c³e=bc³, c²de=bc²d, d²e=bd², c²e²=c², ce³=ce, e⁴=e², b²f=f, cdf=df, d²f=ad², def=bdf, c²f²=d², df²=ad², e²f²=f², f³=acf², b²g=g, c²g=bc³, cdg=bc²d, d²g=bd², deg=cd, ce²g=cg, dfg=bdf, f²g=cef², cg²=c³, eg²=bc³, dg³=bdg², fg³=bfg², g⁵=bg⁴, b²h=h, ch=c², dh=cd, e³h=eh, fh=cf, gh=cg, e²h²=h², h³=c³, b²i=i, di=d², e²fi=fi, fg²i=c³fi, g⁴i=bg³i, i²=d², b²j=j, c³j=c³, dj=dg², ce²j=cj, e³j=ej, f²j=d², cfgj=bc²fj, fg²j=c³f, g³j=bg²j, e²hj=hj, h²j=bcgj, g²ij=c³i, cj²=c³, ej²=bc²j, g²j²=g²j, hj²=c³, fij²=bc²efij, j³=g²j, b²k=k, c²k=bcegj, d²k=bd², cdek=c²d, de²k=bcde², dfk=bdf, f²k=bcf², cgk=c³, g²k=bc³, h²k=bcegj, e²jk=jk, cefjk=bcfjk, gjk=bcgj, ehjk=bhjk, j²k=bc³, ck²=cegj, dek²=bc²d, e³k²=ek², dgk²=cdk, egk²=c³, fgk²=fgj², hk²=cegj, gik²=gij², jk²=cegj, k³=bc³, b²l=l, dl=df, c²fl=cfl, cefl=bcfl, e²fl=fl, f²l=acf², cgl=bc³l, fgl=bcfl, g³l=bg²l, ce²il=cil, e³il=eil, cfil=adf, g²il=c³il, e²hil=hil, h²il=be²gil, c²jl=beh²l, fjl=cfl, gjl=bc³l, e²ijl=ijl, ij²l=be²gil, fkl=bcfl, e²gkl=c³l, hkl=bj²l, egikl=bc³il, jkl=bhjl, ek²l=eh²l, gk²l=egkl, ik²l=be²gil, l²=d², b²m=m, cm=bc², d²m=bd², dem=bcde, e³m=em, dfm=bdf, f²m=bcf², dgm=dg², egm=bceg, g²m=bg²j, hm=bc², fgim=bcfgi, ejm=bcej, fgjm=c²fj, fijm=bcfij, j²m=bg²j, dkm=c²d, e²km=km, gkm=bc³, jkm=bcjk, k²m=bc³, flm=bcfl, glm=c³l, e²ilm=ilm, ijlm=bcijl, klm=bce²kl, dm²=dg², fgm²=bc³f, gim²=gij², fjm²=c²fj, gjm²=bg²j, ijm²=c²ij, km²=bc³, jlm²=beh²l, m³=bg²j, b²n=n, c²n=cegj, dn=dgk, ce²n=cn, f²n=bcef², cgn=bc³, e³gn=egn, fgn=cfjk, g³n=bc³, hn=cn, e³in=ein, g²in=c³i, cjn=cegj, fjn=efgj, gjn=bc³, e²ijn=ijn, j²n=c³, ckn=hjk, e³kn=ekn, gkn=c³, jkn=bcegj, k²n=bhjk, cln=e³gl, e³ln=eln, fln=cfl, gln=bc³l, e²iln=iln, jln=e³gl, ekln=be²gl, ikln=begil, e²mn=mn, gmn=c³, jmn=bcegj, kmn=bhjk, lmn=be³gl, m²n=c³, e³n²=en², fn²=bc²efj, egn²=c³, g²n²=c³, gin²=gij², jn²=c³, kn²=bcn², ln²=be²gl, mn²=bcn², n³=c³, b²o=o, c²o=c²d, do=d², fo=df, cgo=bc²d, e²go=cde, g⁴o=dg², ho=co, io=d², cjo=c²d, ejo=ceo, gjo=g³o, j²o=dg², cko=cdk, e²ko=bce²o, gko=dgk, jko=bc²d, k²o=dk², lo=df, emo=bceo, gmo=dg², jmo=bdg², kmo=c²d, m²o=dg², cno=cde², e³no=eno, egno=c²d, ekno=bcde, mno=bcde², n²o=dek, o²=d², b²p=p, c²p=c³, dp=dg², cep=bcp, e³p=ep, cfp=bcfjk, f²p=d², cgp=bc³, egp=c³, fgp=fgj², g²p=g²j, hp=cp, cjp=c³, ejp=cgj, gjp=gm², fijp=bc²efij, j²p=g²j, kp=bcp, e²lp=belp, flp=cfl, glp=bc³l, eilp=bilp, jlp=begkl, emp=cp, gmp=g²j, fimp=cfijk, jmp=bg²j, ilmp=bcilp, m²p=g²j, np=bcgj, op=dg², cp²=c³, ep²=bc³, fp²=bfgj², gp²=bg²j, ip²=bgij², jp²=g²j, lp²=begkl, mp²=bg²j, p³=g²j, b²q=q, c²q=bc³, cdq=cdk, d²q=bd², ceq=bc²ej, deq=dk², dfq=bdf, f²q=bd², cgq=c³, e²gq=bcgj, efgq=bfjp, dg²q=bc²d, fg²q=bc³f, g³q=g²n, ehq=cegj, h²q=bc³, cfiq=bc²fij, fgiq=c²fij, g²iq=bc³i, hiq=bgijm, cjq=bc³, ejq=bc²ej, fjq=bc²fj, gjq=g²n, hjq=bc³, ijq=bc²ij, j²q=bc³, ckq=c³, dkq=dk², ekq=cgj, fkq=fj², hkq=c³, ikq=ijp, jkq=c³, k²q=bc³, e³lq=elq, flq=bcfl, glq=begkl, hlq=egkl, cilq=begil, e²ilq=ilq, jlq=eh²l, klq=begkl, dmq=c²d, emq=c²ej, fmq=c²fj, gmq=bc³, imq=c²ij, jmq=c³, kmq=bc³, lmq=beh²l, m²q=bc³, cnq=bc³, enq=bcgj, fnq=bfjp, inq=bijp, jnq=g²nq, knq=c³, lnq=egkl, mnq=c³, n²q=bc³, coq=cdk, eoq=c²d, g²oq=gno, joq=gno, koq=dk², moq=g²no, gnoq=dk², pq=bc³, cq²=c³, dq²=c²d, eq²=bc³, fq²=c³f, hq²=c³, giq²=gij², jq²=g²q², kq²=bc³, lq²=begkl, mq²=g²nq, nq²=c³, goq²=noq, q³=bc³>

P = {a, b², c, c², c³, bd, acd, ac²d, d², be, bce, bc²e, ade, e², ce², bde², acde², be³, ade³, f, acf, ac²f, ac³f, bdf, aef, bcef, abc²ef, e²f, ace²f, ae³f, f², cf², bef², bcef², bg, bcg, dg, eg, ceg, be²g, e³g, bfg, abcfg, aefg, acefg, be²fg, ae³fg, g², bdg², fg², bg³, g⁴, h, beh, e²h, h², beh², bi, aci, ac²i, ac³i, aei, abc²ei, be²i, ace²i, ae³i, fi, c²fi, c³fi, aefi, cefi, bf²i, acf²i, aef²i, abcgi, acegi, bcfgi, befgi, bg²i, ahi, ae²hi, ah²i, abeh²i, j, cj, c²j, bej, bcej, bc²ej, e²j, afj, acfj, ac²fj, abefj, abcefj, abc²efj, ae²fj, bgj, bcgj, egj, cegj, be²gj, bfgj, aefgj, abe²fgj, g²j, hj, behj, aij, acij, ac²ij, abceij, abc²eij, ae²ij, bfij, bcfij, efij, bc²efij, abcgij, aegij, acegij, abe²gij, fgij, ahij, abehij, j², fj², bgj², bfgj², bij², bk, bck, adk, ek, cek, bdek, be²k, bce²k, e³k, bfk, bcfk, efk, acefk, abe²fk, abce²fk, e³fk, gk, adgk, begk, e²gk, be³gk, afgk, befgk, ae²fgk, abe³fgk, bhk, ehk, be²hk, beik, aceik, abe²ik, abce²ik, befik, bcefik, agik, ae²gik, abe³gik, aehik, abe²hik, bjk, bcjk, ejk, cejk, abfjk, abcfjk, aefjk, bhjk, abijk, abcijk, aeijk, aceijk, befijk, abhijk, k², bdk², bek², e²k², fk², abefk², ae²fk², bgk², bik², abeik², ae²ik², fik², l, acl, ac²l, ac³l, ael, bcel, abc²el, e²l, ace²l, ae³l, fl, cfl, befl, bgl, aegl, be²gl, ae³gl, g²l, ahl, behl, ae²hl, ah²l, abeh²l, il, c²il, c³il, ceil, e²il, abfil, aefil, bgil, be²gil, ehil, ajl, acjl, bejl, abcejl, ae²jl, ahjl, abehjl, bijl, bcijl, eijl, j²l, bkl, bckl, ekl, acekl, abe²kl, abce²kl, e³kl, agkl, begkl, beikl, k²l, bm, dm, em, be²m, abfm, efm, abe²fm, gm, fgm, abim, abe²im, efim, bjm, bfjm, gjm, ijm, km, bekm, afkm, abefkm, aikm, abeikm, ablm, elm, abe²lm, eilm, bjlm, m², bem², e²m², fm², abefm², ae²fm², bgm², bim², abeim², ae²im², fim², befim², jm², lm², abelm², ae²lm², ilm², beilm², n, cn, ben, bcen, e²n, be³n, afn, acfn, befn, abcefn, ae²fn, abe³fn, bgn, egn, be²gn, g²n, bin, acin, aein, bfin, aefin, cefin, abe²gin, jn, bejn, e²jn, aijn, bkn, ekn, be²kn, bfkn, aefkn, abe²fkn, abe²ikn, fikn, befikn, ln, beln, e²ln, bkln, bmn, emn, abfmn, aefmn, abimn, efimn, n², cn², ben², bcen², e²n², bgn², bin², acin², aein², bo, aco, aeo, be²o, ace²o, ae³o, go, aego, bg²o, g³o, bjo, ako, beko, mo, bno, ag²no, ajno, p, cp, bep, e²p, afp, abefp, ae²fp, bgp, aip, acip, abeip, ae²ip, bfip, efip, jp, fjp, bijp, alp, aclp, abelp, bilp, bmp, bfmp, blmp, p², bq, bcq, adq, eq, be²q, e³q, bfq, bcfq, aefq, abe²fq, ae³fq, gq, adgq, begq, afgq, bg²q, bhq, iq, aeiq, abe²iq, ae³iq, bjq, kq, bgkq, blq, bclq, aelq, abe²lq, mq, bnq, gnq, bg²nq, oq, bgoq, noq, q², bgq², g²q², biq², boq²}

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

Monoid Structure