Details Page for 0.4107

Complete Solution is Known:

MSV File: q-0.4107.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₁(0.4107):

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,y,z,A,B,C,D,E,F,G,H | a²=1, b⁵=b³, b³c²=b³, b²c³=b²c, c⁴=c², bd=ab³, c³d=cd, d²=b⁴, be=ab, ce=ac, de=ad, e³=ae², bf=b⁴, c³f=cf, df=ab³, ef=af, f²=b⁴, b³g=ab⁴c, bcg=ab²c², c²g=abc³, dg=ab²g, eg=ag, cfg=ab⁴, g²=b², b²h=ab³, bc³h=bch, dh=b³, eh=ah, fh=ab⁴, bgh=ab²g, cgh=abc²h, h²=b⁴, b³i=b³c, bc²i=bi, c³i=ci, c²di=di, ei=ai, fi=b³c, bgi=ab²ci, cgi=abi, c²hi=hi, ghi=abchi, i²=b²ci, bj=ab³, c³j=cj, c²dj=dj, ej=aj, fj=ab³, gj=ab²g, hj=b³, ij=bhi, j²=b⁴, bk=bc, c²dk=dk, ek=ak, fgk=ab⁴, c³hk=chk, ghk=abc²h, c²ik=ik, dik=bchi, gik=abi, hik=chi, c²jk=jk, djk=b⁴c, k²=ck, bl=ab²c, c³l=cl, dl=b³c, el=al, fl=ab⁴c, cgl=b²c, hl=abch, c²il=il, gil=b²i, jl=b³c, kl=cl, l²=b²ci, b²m=ab³c, bc²m=bm, c³m=cm, dm=b³c, em=am, fm=ab⁴c, gm=abcm, bhm=b³c, c²hm=hm, bim=ab²ci, c²im=im, jm=b³c, km=cm, lm=abcm, m²=b⁴, bn=b², dn=ab³, en=an, fn=b⁴, cgn=ab²c², hn=bh, in=acil, jn=ab³, kn=cn, ln=ab²i, mn=bm, n²=b⁴, b²o=b³, bc²o=bo, do=ab³, eo=ao, fo=b⁴, bgo=ab³c, cgo=abo, ho=abo, bio=chim, c²io=io, gio=ahim, jo=ab³, ko=co, lo=achim, mo=abco, no=b⁴, o²=b⁴, bp=ab³, cp=ab²c, dp=b⁴, ep=ap, fp=ab³, gp=ab²g, hp=b³, ip=ab²i, jp=b⁴, kp=ab²c, lp=b³c, mp=b³c, np=ab³, op=ab³, p²=b⁴, b²q=b²i, bcq=aim, c³q=cq, c²dq=dq, eq=aq, fq=b³c, gq=im, bhq=achim, c²hq=hq, biq=b³, c²iq=iq, diq=adj, hiq=ab³, jq=bhi, c²kq=kq, dkq=bchi, hkq=chq, ikq=b²i, c²lq=lq, ilq=ab³c, bmq=ab⁴, c²mq=mq, hmq=him, imq=ab³c, cnq=alq, oq=io, pq=ab²i, bq²=b³, c²q²=q², dq²=adj, hq²=ab³, iq²=b⁴c, kq²=b²i, lq²=ab³c, mq²=ab³c, nq²=b³, q³=b⁴c, b²r=b⁴c, cr=b², dr=ab⁴c, er=ar, fr=ab²g, hr=abr, ir=b²ci, jr=ab⁴c, kr=b², lr=ab³, mr=ab³, nr=b³c, or=ab²g, pr=ab⁴c, qr=b²ci, r²=b⁴, bs=acjk, ds=ab³, es=as, fs=b⁴, gs=jk, c²hs=hs, c²is=is, his=bhi, js=ab³, ks=cs, ls=bhi, ms=chs, ns=b⁴, os=b⁴, ps=ab³, c²qs=qs, hqs=achim, iqs=b³, q²s=b³, rs=b³c, s²=b⁴, bt=ab²i, c³t=ct, dt=b³c, et=at, ft=ab⁴c, cgt=b²i, ht=hm, c²it=it, git=b⁴c, jt=b³c, kt=ct, lt=b⁴, mt=b⁴, nt=ab⁴c, ot=ab⁴c, pt=b³c, qt=it, rt=ab³, st=ab⁴c, t²=b⁴, b²u=abo, c³u=cu, du=bo, eu=au, cgu=abc²u, bc²hu=bhu, bhiu=chim, ju=bo, ku=cu, c²lu=lu, glu=abo, bmu=bchu, c²mu=mu, hmu=ab⁴c, imu=chiu, c²nu=nu, gnu=bco, ou=fu, pu=bo, bqu=ahiu, hqu=b³c, iqu=ahim, mqu=b³, nqu=aclqu, q²u=ahim, su=nu, tu=clqu, u²=b⁴, bv=b²ci, c³v=cv, dv=ab³, ev=av, fv=b²ci, cgv=ab²ci, c²hv=hv, ghv=b³c, civ=ait, giv=bgr, hiv=achim, jv=ab³, kv=cv, lv=ab⁴c, mv=ab⁴c, nv=b⁴, ov=b²ci, pv=ab³, qv=acit, rv=b³c, sv=b⁴, tv=ab⁴c, huv=him, iuv=bru, v²=b⁴, bw=ab⁴c, c³w=cw, dw=b³c, ew=aw, fw=ab⁴c, gw=bgru, hw=hm, iw=it, jw=b³c, kw=cw, lw=b⁴, mw=b⁴, nw=ab⁴c, ow=ab⁴c, pw=b³c, qw=it, rw=ab³, sw=ab⁴c, tw=b⁴, uw=b³c, vw=ab⁴c, w²=b⁴, b²x=bru, bcx=abgru, c²x=cfu, dx=abru, ex=ax, cfx=ab⁴, cgx=afx, fgx=b³, bhx=abru, chx=bgru, bix=ab⁴, cix=ab³c, gix=fgu, hix=b⁴, jx=abru, fkx=abgru, hkx=bgru, ikx=ab³c, lx=bgru, mx=bgru, cnx=abgru, gnx=gru, ox=agkx, px=abru, qx=ghx, brx=abgru, sx=agrx, tx=b⁴, ux=b³c, vx=aguv, wx=b⁴, x²=b⁴, by=br, c²y=b²i, dy=ab⁴c, ey=ay, fy=br, cgy=b²g, hy=abr, ciy=b⁴c, giy=b²g, jy=ab⁴c, ky=cy, ly=ab³, my=ab³, ny=b³c, oy=br, py=ab⁴c, qy=abgr, ry=b⁴, sy=b³c, ty=ab³, cuy=ahim, iuy=abgru, vy=b³c, wy=ab³, cxy=bru, ixy=bru, y²=b⁴, bz=abgx, dz=bgru, ez=az, fz=ab³, cgz=b³, hz=aghx, ciz=ahim, giz=b³, jz=bgru, kz=cz, lz=b³c, mz=b³c, nz=agru, oz=ab³, pz=bgru, qz=achim, rz=agrx, sz=ab³, tz=b³c, uz=him, vz=ab³, wz=b³c, xz=b³c, yz=agxy, z²=b⁴, bA=ab⁴c, cA=ab³, dA=b³c, eA=aA, fA=ab⁴c, hA=b⁴c, iA=ab³, jA=b³c, kA=ab³, lA=b⁴, mA=b⁴, nA=ab⁴c, oA=ab⁴c, pA=b³c, qA=ab³, rA=ab³, sA=ab⁴c, tA=b⁴, uA=abru, vA=ab⁴c, wA=b⁴, xA=bgru, yA=ab³, zA=b³c, A²=b⁴, bB=abco, cB=nu, dB=b³c, eB=aB, fB=ab⁴c, hB=bchu, iB=ailu, jB=b³c, kB=nu, lB=him, mB=bhu, nB=ab⁴c, oB=ab⁴c, pB=b³c, qB=alqu, rB=ab³, sB=ab⁴c, tB=b⁴, uB=abru, vB=ab⁴c, wB=b⁴, xB=bgru, yB=ab³, zB=b³c, AB=b⁴, B²=b⁴, b²C=b³, bcC=ac³z, c³C=cC, dC=ab³, eC=aC, fC=b⁴, gC=c³z, hC=abo, iC=io, jC=ab³, kC=cC, lC=achim, mC=abco, nC=b⁴, oC=b⁴, pC=ab³, qC=io, rC=b³c, sC=b⁴, tC=ab⁴c, uC=alqu, vC=b⁴, wC=ab⁴c, xC=ab⁴c, yC=b³c, zC=ab³, AC=ab⁴c, BC=ab⁴c, C²=b⁴, bD=ab³, cD=ab⁴c, dD=b⁴, eD=aD, fD=ab³, gD=ab²g, hD=b³, iD=ab⁴c, jD=b⁴, kD=ab⁴c, lD=b³c, mD=b³c, nD=ab³, oD=ab³, pD=b⁴, qD=ab⁴c, rD=ab⁴c, sD=ab³, tD=b³c, uD=bgru, vD=ab³, wD=b³c, xD=abru, yD=ab⁴c, zD=bgru, AD=b³c, BD=b³c, CD=ab³, D²=b⁴, bE=agrx, c²E=ab³c, dE=b³c, eE=aE, fE=ab⁴c, gE=gA, hE=grx, iE=ab³, jE=b³c, kE=cE, lE=b⁴, mE=bgru, nE=ab⁴c, oE=ab⁴c, pE=b³c, qE=ab³, rE=ab³, sE=ab⁴c, tE=b⁴, uE=abru, vE=ab⁴c, wE=b⁴, xE=bgru, yE=ab³, zE=b³c, AE=b⁴, BE=b⁴, CE=ab⁴c, DE=b³c, E²=b⁴, b²F=b³, bcF=bco, c³F=cF, dF=ab³, eF=aF, fF=b⁴, gF=abco, hF=abF, iF=io, jF=ab³, kF=cF, lF=achim, mF=abco, nF=b⁴, oF=b⁴, pF=ab³, qF=io, rF=b³c, sF=b⁴, tF=ab⁴c, uF=ab³, vF=b⁴, wF=ab⁴c, xF=ab⁴c, yF=b³c, zF=ab³, AF=ab⁴c, BF=ab⁴c, CF=b⁴, DF=ab³, EF=ab⁴c, F²=b⁴, bG=b³c, c³G=cG, dG=acdj, eG=aG, fG=b³c, gG=ab³, hG=ab³c, ciG=cdj, jG=ab⁴c, kG=him, lG=ab³, mG=ab³, nG=b³c, oG=b³c, pG=ab⁴c, qG=b⁴, rG=b⁴, sG=b³c, tG=ab³, uG=ab⁴c, vG=b³c, wG=ab³, xG=ab³, yG=b⁴, zG=ab⁴c, AG=ab³, BG=ab³, CG=b³c, DG=ab⁴c, EG=ab³, FG=b³c, G²=b⁴, bH=achim, c²H=H, dH=b³c, eH=aH, gH=him, hH=afH, iH=ab³, jH=b³c, kH=c²uv, lH=b⁴, mH=b⁴, nH=ab⁴c, oH=achim, pH=b³c, qH=ab³, rH=ab³, sH=ab⁴c, tH=b⁴, uH=b³c, vH=ab⁴c, wH=b⁴, xH=b⁴, yH=ab³, zH=b³c, AH=b⁴, BH=b⁴, CH=ab⁴c, DH=b³c, EH=b⁴, FH=ab⁴c, GH=ab³, H²=b⁴>

P = {a, b², b⁴, c², b²c², acd, e², ah, abch, b²ci, achi, cj, ck, c³k, adk, al, abcm, hm, ao, ac²o, acio, cq, adq, achq, kq, q², abgr, as, ac²s, acis, acqs, at, abu, abc²u, hu, c²hu, abciu, giu, chiu, clu, cmu, abru, achv, acuv, aw, ackx, cy, iy, aA, aB, bC, ac²C, cE, bF, ac²F, ac²G, iG, acfH}

Phi = 1 1 a a b b ab c c d e f g h b i ab² j k l m n o p q r abo anq b³ s t abm cq² u cjk v w x b³ y agt z b²i A B b³ C D b⁴c bco abF E b³ F ab³c grx G abF abF b³ ab³c H b³ b⁴c ab⁴ cfH b⁴c ab³c ab³c b³ b³ ab⁴ b⁴c b⁴c ab⁴ ab³c b³ b³ ab³c b⁴c b⁴c ab⁴ ab⁴ b³ ab³c ab³c b³ b⁴c ab⁴ ab⁴ b⁴c ab³c ab³c b³ b³ ab⁴ b⁴c b⁴c ab⁴ ab³c b³ b³ ab³c b⁴c b⁴c ab⁴ ab⁴ b³ ab³c ab³c b³ b⁴c ab⁴ ab⁴ b⁴c ab³c ab³c b³ b³ ab⁴ b⁴c b⁴c ab⁴ ab³c b³ b³ ab³c b⁴c b⁴c ab⁴ ab⁴ b³ ab³c ab³c b³ b⁴c ab⁴ ab⁴ b⁴c ab³c ab³c b³ b³ ab⁴ b⁴c b⁴c ab⁴ ab³c b³ b³ ab³c b⁴c b⁴c ab⁴ ab⁴ b³ ab³c ab³c b³ b⁴c ab⁴ ab⁴ b⁴c ab³c ab³c b³ b³ ab⁴ b⁴c b⁴c ab⁴ ab³c b³ b³ ab³c b⁴c b⁴c ab⁴ ab⁴ b³ ab³c ab³c b³ b⁴c ab⁴

Monoid Structure