Details Page for 0.2454

Complete Solution is Known:

MSV File: q-0.2454.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₃₈(0.2454):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v | a²=1, b⁴=b², bc²=b, c³=c, b²d=ab²c, c²d=d, d⁴=acd³, b²e=b²c, c²e=e, bd²e=b³c, d³e=acd²e, e²=b², b²f=ab², c²f=f, bdf=abcde, d³f=acd²f, bef=bcde, d²ef=acdef, f²=b², c²g=g, bdg=abcg, beg=b³cg, bfg=ab³g, b²g²=b², d²g²=acdg², defg²=acefg², bg³=bg, deg³=acd²eg, dfg³=acd²fg, efg³=acdefg, g⁴=g², bh=ab², c²h=h, dh=abcde, eh=bcde, fh=abde, gh=ab³g, h²=b², b²i=ab², c²i=i, bdi=abcde, d²i=ab², bei=bcde, dei=b², fi=b², bgi=ab³g, egi=adgi, g²i=ab², hi=abde, i²=b², b²j=ab³g, c²j=j, d³j=acd²j, bdej=b²g, d²ej=acdej, bfj=abcej, d²fj=acdfj, defj=acefj, bgj=ab², degj=b³, fgj=acegj, g²j=abg, hj=abcej, ij=b³g, bej²=aegj, gj²=abj, bj³=bj, ej³=ej, fj³=fj, dj⁴=dj², j⁵=j³, bk=b³g, c²k=k, dgk=acgk, egk=aefg², fgk=ab², g³k=gk, hk=ab³g, ik=gi, jk=ab³, dk²=ack², gk²=b²g, fk³=d²fk, k⁴=k², b²l=ab³c, c²l=l, bdl=abcl, bel=ab², del=b³c, bfl=b²c, dfl=bde, efl=b³, bgl=acdefg, dgl=acgl, egl=ab³g, fgl=b³cg, hl=b²c, bil=b²c, dil=bde, eil=b³, gil=b³cg, bjl=efj, ejl=abcej, fjl=bej, dkl=ackl, ekl=ab³g, fkl=b³cg, gkl=ab³c, k²l=ab³c, l²=b², bm=ab², c²m=m, d²m=acdm, em=ab³c, fm=b³, gm=ab³g, hm=b², im=b³, j³m=jm, km=ab³g, dlm=aclm, m²=b², bn=ajlm, c²n=n, d²n=acdn, en=b²g, fn=ab²cg, dgn=acgn, g²n=cdefg, hn=ab³cg, in=ab²cg, gjn=jlm, j³n=jn, kn=b²c, ln=cjlm, mn=ab³cg, n²=b², bo=b³g, c²o=o, d³o=acd²o, eo=dgi, fo=ab²g, go=b², ho=ab³g, io=ab²g, jo=cegj, ko=b², lo=ab³cg, mo=ab³g, no=b²c, o²=b², b²p=ab²cg, c²p=p, bd²p=ab³cg, d³p=acd²p, bep=abdp, dep=b²cg, bfp=bcdp, dfp=ab²g, efp=b²g, bgp=ab³c, d²gp=efg², fgp=acegp, dg²p=defg, hp=bcdp, ip=b²cg, fjp=acejp, gjp=abp, bj²p=bp, d²j²p=ab²cg, ej²p=adj²p, dj³p=aejp, kp=ab²c, blp=b²g, elp=bcdp, flp=abdp, glp=b³, dj²lp=abcdp, j³lp=abcjp, mp=bcdp, np=acdjlp, op=adjlp, p²=b², bq=ab²g, c²q=q, dq=b³cg, eq=ab³cg, fq=b³g, gq=ab³, hq=b²g, iq=b³g, jq=b², kq=ab³, mq=b²g, nq=ab³c, oq=ab³, q²=b², b²r=b³cg, c²r=r, dr=acr, ber=b²g, bfr=ab²cg, gr=d²jp, hr=ab²cg, ir=ab³cg, jr=ab²c, kr=d²jp, blr=efr, elr=ab²cg, flr=b²g, mr=abr, nr=b³, or=b³c, pr=acd²jp, qr=ab²c, r²=b², b²s=ab³c, c²s=s, bd²s=clpq, d³s=b³, bdes=aclpq, d²es=ab³, dfs=cd²s, efs=cdes, bgs=ab²cg, dgs=b³g, egs=ab³g, g²s=ab³c, hs=bcds, is=fs, js=b²cg, ks=gs, bls=b³, dls=bces, els=aclpq, gls=b²g, ms=b²c, ns=ab³g, os=ab³cg, ps=b³g, qs=b²cg, rs=ab²g, s²=b², b²t=ab²g, c²t=t, d³t=b²cg, bdet=abd²t, d²et=ab²cg, dft=cd²t, eft=cdet, bgt=ab³, d²gt=lpq, degt=alpq, fgt=bcfs, g²t=ab²g, ht=bcdt, it=ft, jt=b³, kt=gt, blt=b²cg, dlt=bcet, elt=abd²t, glt=b³c, mt=b³g, nt=clpq, ot=abcfs, pt=bfs, qt=b³, rt=ab³c, st=b³cg, t²=b², b³u=bu, c²u=u, bdu=abcu, d²u=acdu, eu=b²cu, fu=ab²u, b²gu=gu, dgu=acgu, g²u=b²u, hu=abu, iu=ab²u, bju=agu, dju=bcgu, gju=abu, j³u=ju, ku=gu, lu=abcu, mu=abu, nu=cgu, ou=gu, pu=acgu, qu=abgu, ru=bcgu, su=abcu, tu=agu, u²=b², b²v=v, c²v=v, dv=acv, ev=cv, fv=av, g²v=v, hv=abv, iv=av, jv=abgv, kv=gv, lv=abcv, mv=abv, nv=cgv, ov=gv, pv=acgv, qv=abgv, rv=bcgv, sv=abcv, tv=agv, v²=b²>

P = {a, b², c², acd, d², acd³, ce, ade, cd²e, acf, df, acd²f, cfg, adfg, cd²fg, g², acdg², ceg², adeg², acfg², dfg², cfg³, ai, cdi, acei, fj, acdfj, cefj, j², acdj², d²j², cej², adej², acfj², dfj², j⁴, afk, cdfk, ad²fk, cgk, k², cek², acfk², acl, dl, acd²l, d³l, acgl, acg²l, acg³l, acj²l, dj²l, acd²j²l, acj⁴l, akl, gp, g³p, abjp, alp, cdlp, ad²lp, cjlp, aj²lp, afr, acefr, bcs, abds, bes, afgs, als, abct, bdt, abcd²t, abet, bcft, lt, aflt, au, cdu, aj²u}

Phi = 1 1 a b a b ab c d e f bc abc g h bce i b j k ch be l b²c ab²c gjl m n ab² bd² ab² o ab³g b²c ab²c b³ b²cg p q r ab² b³ ab² b³ ab³ b²c abdp b³g ab² b³c b²u b²g bcdp b³ ab² b³ ab³g b²g b²u s t b³cg ab²c b²c ab³ b²cg u b³ b²u b²g ab³g abu b²c b³ b²cg ab²cg b²u b³cg ab² abcu ab² b²g ab³ b²c ab³g b³g ab² b³cg ab³cg b²g b²u ab²cu ab² b³ ab³g b²g b²u ab³c ab²g b³cg agu abu ab³g b²cg bgu b³ ab²g b²g ab³g abu agu b³ b²cg ab²cg b²u b³cg ab² abcu ab² ab²cu ab³ ab³g b²u agu ab² b³cg ab³cg ab³c b²cu abcgu b²cu b²c ab³g b²g b²u ab³c ab²g b³cg v ab²cg ab³g b²cg bgu b³ ab²g b²g ab² abu v b³ b²cg ab²cg b²u b³cg ab² bcu ab² ab²cu ab³ ab³g b²u agu ab² b³cg ab³cg ab³c ab²cu v cv b²c ab³g b²u b²g abcgu ab² b³cg v av b²c b²cg abv b³ b²u b²g ab² abu cgu b³ b²cg ab²cg b²u abcgu ab² agu ab² abu acv bgu b³ b²u ab² b³cg agu b³cg b²cu b³c bgu b³ ab³g acv bcv agu ab² b³cg bgu av b²c bcu v b³ bcgu b²g abcgu abu cgu b³ ab³g b³ ab²cg b²g abcgu v ab² abu b²u bgu b³ abcgu v ab² agu b²g gv bgu b²u b³ bgv acv ab³g agu ab²g b²g bgu av ab³g buv v abv ab³c ab²cu ab² acv cgu b³ ab³g b³ bv b²g ab³c ab² ab³c b³cg b²u b³ ab³g b³ agu uv ab² b²g bgu v bgu b³ bgv abcgu ab³g agu b²g bgu v bgu ab³g b³ abv abgv ab³c b²g b²u b²g cgu abcgv ab³g b³ bv b²u v ab² b³cg abu bcv b²c ab³g b³ agu b²u ab² b³cg bgu cgu ab²cu b³ ab²cg acv acgv agu abv b²g bgu ab²cu ab³g b³ v abv b²u b²g ab³c b²g abcgv bgu ab³g agu bgv b²u ab³c ab² uv abu acgu b²c ab³g ab²cg abcgu acv ab² b³cg gv acguv v ab²cu ab²cg acv acgv bcu abv b²g v ab²cu bgu b³ b²c bcu b²u b²g ab³c b²g bgu abu ab³g abu acv b²u auv ab² v abu abcguv b²c ab²cg b³ abcgv acv b²u bcv ab³c gv ab²cg ab²cu ab²cg b²c b²u bcu ab² b²g v ab²cu ab³g

Monoid Structure