Details Page for 0.7315

Complete Solution is Known:

MSV File: q-0.7315.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₂₈(0.7315):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x | a²=1, b⁵=b³, b³c²=b³, c⁴=c², b²d=ab⁴, bc²d=bd, c³d²=cd², d³=ad², b³e=b³c, bd²e=abde, b²e²=b⁴, bc²e²=be², c³e²=ce², bde²=abe², d²e²=ade², be³=b³c, ce³=b⁴, de³=ae³, e⁴=b⁴, bf=b², df=bd, e²f=be², cf²=b⁴c, ef²=b⁴c, f³=b³, bg=b²c, dg=bde, c³eg=ceg, e²g=b³c, fg=b²c, g²=b⁴, b²h=ab⁴, c³dh=cdh, bc²eh=beh, c³eh=ceh, de²h=ae²h, fh=bh, c²gh=gh, egh=be²h, bh²=abh, dh²=adh, e²h²=ae²h, gh²=agh, h³=ah², b²i=b³, bc²i=bi, di=abd², c²ei=ei, e²i=be², fi=b⁴, c²gi=gi, egi=bcei, bhi=ab⁴, ehi=beh, ghi=ab⁴c, h²i=ahi, i²=b⁴, bj=b²c, c³dj=cdj, d²j=adj, ce²j=abe²h, de²j=ae²j, fj=b²c, c²gj=gj, c³hj=chj, e²hj=ae²j, ghj=ab⁴, h²j=ahj, ij=gi, j²=gj, b²k=ab⁴, c²k=k, bdk=b³, d²k=ab⁴, e²k=ab⁴, fk=bk, gk=ab³c, bhk=abk, dhk=adk, h²k=ahk, bik=ab⁴, eik=bek, hik=aik, jk=cik, dk²=adk, bek²=b³c, hk²=ak², ik²=bk², bk³=bcek, ek³=aek², k⁵=ak⁴, b²l=ab³, dl=bd², c²el=el, e²l=abe², fl=bl, gl=bel, bhl=abl, h²l=ahl, il=bl, c²jl=jl, ejl=bcel, hjl=ajl, kl=aik, l²=b⁴, b²m=b³c, bc²m=bm, c³m=cm, bdm=bel, d²m=adj, bem=b⁴, dem=dej, e²m=e²j, fm=bm, gm=abcel, h²m=ahm, bim=b³c, c²im=im, eim=b⁴, him=bel, jm=cegj, bkm=bel, dkm=b³c, ekm=ab³, hkm=akm, ikm=ab⁴c, k²m=b³c, lm=jl, m²=b⁴, b³n=ab³, dn=ab²n, be²n=ab³, ce²n=ab⁴c, e³n=ab⁴c, f²n=e²n, c³gn=cgn, bhn=abcek, ehn=abel, ghn=b³c, h²n=ahn, c²in=in, ein=c²efn, gin=b²c³n, hin=abcek, e²jn=ab³c, gjn=ab⁴, hjn=abek, kn=abin, ln=abcek, bmn=b²c²en, c²mn=mn, emn=ab³, hmn=b³c, imn=b²c²en, n²=b⁴, b²o=b⁴c, do=bel, eo=cegj, fo=bo, go=b³, bho=abo, h²o=aho, io=bo, jo=b³, ko=bel, bc²lo=bel, chlo=aclo, mo=b³, bno=ab³c, c²no=bel, hno=ablo, o²=b⁴, bp=b²n, c³dp=cdp, d²p=adp, cdep=be², ce²p=ab³c, de²p=ae²p, e³p=ab³c, fp=b²n, cgp=ab⁴, egp=ab⁴, c³hp=chp, dehp=ae²j, e²hp=e³j, ghp=b⁴c, h²p=ahp, cip=bcin, eip=b²c²en, gip=ab³c, hip=b⁴, jp=ab⁴c, dkp=ab³, ekp=b³c, hkp=akp, ikp=b⁴, k²p=bcek, lp=ae²n, cmp=b²c³en, dmp=b⁴c, emp=ab⁴, hmp=b⁴c, imp=ab³c, kmp=b⁴c, np=b³, op=ab³c, p²=b⁴, b²q=b²c²n, c²q=q, dq=ab²c²n, e²q=b²c³en, f²q=ab⁴, bhq=b³, ehq=ab²c²en, ghq=b³c, h²q=bcel, iq=ab³, jq=bcq, kq=ab²c²n, lq=b³, bmq=b²c²en, emq=ab³, hmq=b³c, nq=b⁴, oq=b²c³n, pq=b³, q²=b⁴, br=b³c, cr=gj, dr=ab⁴c, e²r=b⁴c, fr=b³c, gr=b³, hr=ab⁴c, ir=b³c, jr=b³, kr=ab⁴c, lr=ab³c, mr=b³, nr=ab⁴c, or=b⁴, pr=ab³c, qr=b²c³n, r²=b⁴, b²s=ab³, bc²s=bs, c³ds=cds, d²s=ads, de²s=ae²s, fs=bs, c²gs=bes, egs=be²s, c³hs=chs, bdhs=abhs, ghs=behs, h²s=ahs, bis=ab³, c²is=is, eis=bes, gis=ab³c, his=bhs, c³js=cjs, gjs=ab³, dhjs=ahjs, ks=kp, ls=bds, ms=adjs, ns=b³, os=ab³c, c³ps=cps, dps=aps, ceps=abe²s, gps=b³c, ehps=e²js, ips=b³, qs=b³, rs=ab³c, s²=b⁴, b²t=ab⁴, bc²t=bt, dt=b⁴, bet=bek, c²et=et, e²t=ab⁴, ft=bt, gt=ab³c, ht=at, bit=ab⁴, c²it=it, eit=bek, jt=cit, bkt=kp, ekt=b⁴c, ikt=kp, k³t=cdek, blt=b⁴, elt=abek, mt=km, nt=b⁴, ot=bel, pt=b³, qt=b⁴, rt=ab⁴c, st=b³, t²=b⁴, bu=b³c, c³u=cu, ceu=cps, deu=aps, e²u=eps, fu=b³c, gu=b³, ehu=hps, h²u=ahu, iu=b³c, ju=b³, ku=aek², lu=ab³c, mu=b³, nu=ab⁴c, ou=b⁴, pu=ab³c, qu=ab⁴c, ru=b⁴, su=ab³c, tu=ab⁴c, u²=b⁴, bv=ahq, dv=b³, e²v=ab³, fv=ahq, gv=b²en, c³hv=chv, cehv=b³, h²v=ahv, iv=b²c²n, cjv=ahq, kv=b³, lv=b⁴, mv=ahjv, nv=b³, ov=ab³c, pv=b⁴, qv=b³, rv=ab³c, sv=b⁴, tv=b³, uv=ab³c, v²=b⁴, b²w=b³c, bc²w=bw, bdw=ab⁴c, c³dw=cdw, d²w=adw, c³ew=cew, dew=dhp, e²w=e²j, fw=bw, gw=b⁴, hw=aw, iw=bw, jw=bcw, dkw=b³c, bekw=bcel, bk²w=bcew, ek²w=b³, k³w=cekw, blw=ab³c, elw=abew, mw=b⁴, nw=cekw, ow=b³, c²pw=pw, dpw=b⁴c, epw=bcel, qw=ab³c, rw=b³, bsw=ab³c, c³sw=csw, dsw=ad²hu, psw=b³c, btw=pw, etw=ekw, k²tw=cekw, uw=b³, vw=ahjv, w²=b⁴, bx=ahq, c³x=cx, dx=b³, e²x=ab³, fx=ahq, gx=ab⁴c, cehx=b³, ch²x=achx, eh²x=aehv, ix=bcel, jx=jv, kx=b³, lx=b⁴, cmx=bcel, hmx=hjv, nx=b³, cox=ab³, hox=b³c, px=ae²n, qx=b³, rx=ab³c, sx=b⁴, tx=b³, ux=ab³c, vx=b⁴, wx=ahjv, x²=b⁴>

P = {a, b², b⁴, ac, ac², b²c², ac³, d², c²d², ae, ace, b²ce, ac²e, ac³e, b²c³e, cd²e, e², c²e², ade², ac²de², f², h, ch, c²h, c³h, ad²h, ac²d²h, eh, ceh, c²eh, acd²eh, ae²h, ac²e²h, ah², ach², ac²h², ac³h², aeh², aceh², ac²eh², bi, bcei, cgi, gj, cegj, k, ck, ek, ahk, achk, aehk, ak², ack², aek², k³, ck³, ak⁴, ack⁴, al, acl, ac²l, ac³l, ael, acel, hl, chl, c²hl, c³hl, ehl, cehl, abm, abcm, bhm, bchm, bn, bcn, bc²n, bc³n, aben, ab²cen, bc³en, fn, cfn, c²fn, c³fn, aefn, c³efn, abin, ajn, ac²jn, ac³ejn, acmn, ao, aco, ac²o, ac³o, ho, cho, c²ho, c³ho, lo, abclo, ac³lo, agp, mp, bq, bcq, beq, bceq, fq, cfq, efq, cefq, amq, bds, ac³es, bcdes, abe²s, acgs, abchs, abehs, ce²hs, e³hs, ais, cdjs, dejs, c²dejs, ahjs, ac²hjs, ps, c²ps, e²ps, ahps, ac²hps, acdu, cd²u, achu, cdhu, acd²hu, av, acv, ac²v, ac³v, ev, ac²ev, ac³ev, chv, ehv, abcw, abew, bckw, clw, c³ltw, ax, acx, ac²x, ex, c²ex, hx, chx, c²hx, ah²x, aemx, ox}

Phi = 1 a b ab a c b d e f g h i j k l m n o p q r s t u v w ahq x

Monoid Structure