Details Page for 0.3576

Complete Solution is Known:

MSV File: q-0.3576.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₉(0.3576):

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 | a²=1, b⁵=b³, b⁴c=b²c, b²c²=c², c³=b²c, b²d=ab⁴, cd=ab²c, d²=b⁴, b²e=b³, ce=b³c, de=bd, e²=b⁴, b³f=ab³, cf=ab²c, df=ab²f, ef=bd, f²=b⁴, b²g=b³, cg=b³c, dg=bd, eg=b⁴, fg=bd, g²=b⁴, b⁴h=b²h, b²ch=ch, c²h=b²h, beh=b²h, fh=dh, gh=eh, h²=c², b²i=b²c, bci=bc², c²i=b²c, di=ab²c, bei=b²c, fi=ab²c, gi=b³c, bhi=bch, chi=b²h, ehi=bch, i²=c², b²j=ab³c, bcj=aci, c²j=ab³c, dj=b³c, ej=ab²c, fj=b³c, gj=ab²c, chj=ab³h, bij=aci, cij=ab³c, hij=ab³h, j²=c², ck=b³c, bdk=ab³k, bfk=aek, gk=ek, hk=eh, ik=b³c, jk=ab²c, k²=c², b³l=bch, cl=b²h, bdl=abch, bfl=ael, gl=el, hl=b²c, il=b²h, jl=ab³h, kl=bch, l²=c², b²m=m, cm=ab²c, dm=am, em=bm, fm=am, gm=bm, hm=ab²h, im=ab²c, jm=b³c, lm=ach, km²=akm, m³=am², cn=ab²h, bdn=ab³n, gn=en, hn=ab²c, in=ab²h, jn=b³h, ln=ac², m²n=amn, n²=c², b⁴o=b²o, co=ab²c, do=ab²o, beo=b²o, bfo=aeo, go=eo, ho=ab²h, io=ab²c, jo=b³c, ko=km, lo=ach, m²o=amo, mno=ab²no, o²=mo, b⁴p=b²p, cp=b³c, bdp=ab³p, bep=b²p, bfp=aep, gp=ep, hp=eh, ip=b³c, jp=ab²c, kp=c², lp=bch, m²p=amp, dnp=ab²np, op=km, b²p²=p², dp²=ap², ep²=bp², fp²=ap², p⁴=c², b²q=ab³c, cq=ij, dq=b³c, beq=ab³c, fq=b³c, gq=ab²c, ehq=ach, biq=aci, eiq=aci, hiq=ab³h, jq=c², kq=ab²c, lq=ab³h, mq=b³c, nq=b³h, oq=b³c, pq=ab²c, q²=c², b³r=br, cr=ab²c, dr=ab²r, er=br, fr=ab²r, gr=br, hr=ab²h, ir=ab²c, jr=b³c, kr=abc², lr=ach, m²r=amr, b²nr=nr, or=abkm, b²pr=pr, npr=anp³, p²r=ac², qr=b³c, r²=c², b⁴s=b²s, cs=b³c, ds=ab²s, es=b³s, fs=ab²s, gs=b³s, hs=abdh, is=b³c, js=ab²c, ks=c², ls=bch, m²s=ams, b²ns=ns, os=km, ps=c², qs=ab²c, rs=abc², s²=c², b²ct=b²h, c²t=ch, bdt=ab³t, b²ft=abet, gt=abft, ht=aeq, bit=bct, cit=ch, eit=bct, jt=ab³h, b²kt=kt, dkt=akt, ekt=bkt, fkt=akt, lt=c², kmt=akt, m²t=amt, b²nt=nt, dnt=ant, ent=bnt, fnt=ant, b²ot=ot, eot=bot, fot=aot, mot=aot, not=mnt, b²pt=pt, dpt=apt, ept=bpt, fpt=apt, mpt=apt, npt=knt, p²t=bmnp³, qt=ab³h, b²rt=rt, mrt=art, nrt=abknt, prt=abch, st=abrt, t²=c², b³u=bu, cu=b³c, du=ab²u, eu=bu, fu=ab²u, gu=bu, hu=abdh, iu=b³c, ju=ab²c, ku=c², lu=bch, mu=ms, nu=ns, ou=km, pu=c², qu=ab²c, ru=abc², su=c², tu=abrt, u²=c², b²v=b³h, cv=bch, ev=bv, fv=dv, gv=bv, bdhv=aci, iv=bch, jv=ach, kv=bv, lv=b³c, mv=ab³h, nv=ab³c, ov=ab³h, pv=bv, qv=ach, rv=ab³h, sv=abdv, tv=b³c, uv=abdv, v²=c², bw=b³h, cw=ch, dw=ab²h, ew=b³h, fw=ab²h, gw=b³h, hw=c², iw=ch, jw=abch, kw=b³h, lw=b²c, mw=ab²h, nw=ab²c, ow=ab²h, pw=b³h, qw=abch, rw=ab²h, sw=b³h, tw=b²c, uw=b³h, vw=bc², w²=c², b²cx=cx, gx=ex, ehx=bhx, ix=cx, jx=abcx, lx=chx, m²x=amx, kmnx=ab⁴knx, mox=ab²ox, mnpx=ab²npx, np²x=achx, qx=abcx, b²rx=rx, mnrx=anrx, mprx=bc²x, b³sx=bsx, msx=abmrx, nsx=abnrx, ctx=b²hx, bftx=aetx, ntx=ac²x, ux=sx, vx=b³hx, wx=b²hx, x²=c², b⁴y=b²y, cy=b³c, dy=ab²y, ey=b³y, fy=ab²y, gy=b³y, hy=b³h, iy=b³c, jy=ab²c, ky=c², ly=bch, my=km, b²ny=ny, oy=km, py=c², qy=ab²c, ry=abc², sy=c², ty=kt, uy=c², vy=b²h, wy=b³h, b²xy=xy, nxy=b⁴knx, y²=c², b²z=z, cz=ab²c, dz=az, ez=bz, fz=az, gz=bz, hz=ab²h, iz=ab²c, jz=b³c, lz=ach, mz=mo, knz=ab⁴kn, oz=mo, pz=kz, qz=b³c, rz=abkz, sz=kz, ktz=akt, ntz=ant, uz=kz, vz=ab³h, wz=ab²h, kxz=ab⁴kx, kz²=akz, tz²=atz, nxz²=anxz, yz²=b²y, z³=z, b⁴A=b²A, cA=b³c, dA=ab²A, eA=b³A, fA=ab²A, gA=b³A, hA=b³h, iA=b³c, jA=ab²c, kA=c², lA=bch, mA=bmp², b²nA=nA, oA=abc², pA=abmp³, qA=ab²c, rA=abc², sA=c², tA=mnp³, uA=c², vA=b²h, wA=b³h, b²xA=xA, nxA=abchx, yA=c², zA=abc², A²=c², b⁴B=b²B, cB=ab²h, eB=bB, fB=dB, gB=bB, hB=ab²c, iB=ab²h, jB=b³h, b³kB=bkB, blB=abc², dlB=ci, kmB=kmn, m²B=amn, b²nB=nB, dnB=anB, knB=bc², mnB=ac², b²oB=oB, moB=ab²no, noB=ac², b²pB=pB, dpB=apB, mpB=mnp, npB=bc², p²B=bnA, qB=b³h, b²rB=rB, mrB=mnr, nrB=ac², prB=anp³, b³sB=bsB, msB=mns, nsB=bc², tB=nt, buB=abmns, vB=ab³c, wB=ab²c, b²xB=xB, dxB=axB, kxB=b⁴knx, mxB=mnx, nxB=c²x, oxB=b²nox, pxB=b²npx, rxB=nrx, sxB=abnrx, yB=akmn, kzB=kmn, nzB=ac², xzB=nxz, z²B=azB, AB=abmnp², B²=c², cC=b²h, b²fC=abeC, gC=eC, hC=b²c, iC=b²h, jC=ab³h, bkC=bkt, ekC=bkt, fkC=dkC, elC=acj, kmC=akt, m²C=amC, b⁴nC=b²nC, dnC=ab²nC, enC=b³nC, fnC=ab²nC, knC=knt, b²oC=oC, eoC=boC, foC=aoC, moC=aoC, b³pC=bpC, dpC=ab²pC, epC=bpC, fpC=ab²pC, mpC=ab²pC, qC=ab³h, b²rC=rC, mrC=arC, sC=abrt, b²tC=tC, dtC=atC, etC=btC, ftC=atC, ktC=bc², ntC=ach, otC=ac², rtC=ac², uC=abrt, vC=b³c, wC=b²c, b²xC=xC, dxC=axC, exC=bxC, fxC=axC, kxC=ktx, nxC=ac²x, oxC=otx, rxC=rtx, txC=c²x, yC=kt, kzC=akt, tzC=ac², xzC=txz, z²C=azC, AC=bp²C, BC=b²nC, C²=c², b⁴D=b²D, cD=b³c, eD=bD, fD=dD, gD=bD, bhD=b²h, dhD=ab³h, iD=b³c, jD=ab²c, kD=alB, lD=bch, mD=ab²D, b²nD=nD, dnD=anD, oD=ab²D, pD=ci, qD=ab²c, rD=abc², sD=ci, b²tD=tD, dtD=atD, ntD=knt, uD=ci, vD=b²h, wD=hD, b²xD=xD, dxD=axD, hxD=b³hx, yD=ci, zD=ab²D, AD=c², BD=nD, CD=tD, D²=c², b³E=bE, cE=cx, bdE=abE, eE=bE, fE=dE, gE=bE, hE=b²hx, iE=cx, jE=abcx, b²kE=kE, dkE=akE, blE=bchx, kmE=axD, dnE=ab²nE, knE=nxD, mnE=ab²nE, b²oE=oE, b²pE=pE, dpE=apE, np²E=achx, mp³E=ap³E, qE=abcx, b²rE=rE, nrE=abnxD, mprE=p³E, sE=kE, b²tE=tE, dtE=atE, ktE=txD, ntE=ac²x, otE=mtE, ptE=txD, rtE=abtxD, uE=xD, vE=b³hx, wE=b²hx, xE=c², yE=xD, kzE=axD, nzE=noE, tzE=atE, z²E=azE, AE=abmp²E, BE=b²nE, b²CE=CE, dCE=aCE, kCE=txD, lCE=c²x, nCE=ac²x, oCE=mtE, prCE=ap³CE, tCE=c²x, zCE=atE, DE=xD, E²=c², b²F=F, cF=b²h, dF=aF, eF=bF, fF=aF, gF=bF, hF=b²c, iF=b²h, jF=ab³h, lF=c², kmF=abch, m²F=mnp², mnF=c², moF=ch, noF=c², mpF=amnp³, qF=ab³h, mrF=ch, sF=kF, tF=c², vF=b³c, wF=b²c, mxF=achx, nxF=ac²x, oxF=achx, kzF=auF, AF=p³F, kBF=np³F, mBF=abnp³F, nBF=ch, oBF=abnp³F, rBF=anp²F, uBF=abc², xBF=ac²x, zBF=abknF, CF=anp²C, DF=bch, kEF=aprxF, mEF=bprxF, nEF=ac²x, oEF=bprxF, p²EF=abprxF, prEF=prxF, F²=c², b²G=G, cG=ab²c, dG=aG, eG=bG, fG=aG, gG=bG, hG=ab²h, iG=ab²c, jG=b³c, kG=knF, lG=ach, mG=c², oG=c², pG=npF, qG=b³c, rG=nrF, sG=knF, ntG=abknF, uG=knF, vG=ab³h, wG=ab²h, txG=zEF, yG=nyF, nzG=anG, tzG=atG, xzG=axG, AG=np³F, BG=nG, nCG=abknF, tCG=ac², xCG=zEF, zCG=aCG, DG=abc², nEG=chx, tEG=zEF, zEG=aEG, CEG=zEF, FG=ach, G²=c²>

P = {a, b², b⁴, c², be, ab²f, ag, bi, hi, cj, bhj, bk, b³k, ek, am, abkm, m², ao, ab²o, fo, mo, bp, b³p, ep, abmp, p², amp², bp³, abmp³, bq, abhq, aiq, ab²r, mr, abpr, bmpr, as, b³s, abms, abct, abnt, bmnt, bu, abhv, bx, abdhx, nx, b²nx, b⁴nx, aenx, ab²fnx, aknx, ab²knx, ab⁴knx, eknx, amnx, bnox, b³nox, fnox, enpx, anrx, tx, b²tx, b⁴tx, aetx, aktx, amtx, botx, artx, b³y, az, abkz, bnxz, btxz, abyz, z², b³A, bB, abdB, kB, adkB, abnB, sB, uB, abxB, abdC, abfC, adkC, lC, b²lC, bnC, b²npC, bnp²C, abtC, amtC, xC, amxC, ap³xC, b³D, hD, bnxD, btxD, lE, adlE, b²nE, anoE, tE, amtE, CE, amCE, bp³CE, arCE, aF, abkF, abpF, ap²F, abp³F, rF, bprF, abuF, xF, akxF, apxF, p²xF, ap³xF, brxF, abprxF, abyF, axyF, zF, bxzF, bnyzF, az²F, xz²F, abBF, EF, bpEF, arEF, azEF, abtG, bnxG}

Phi = 1 a b a b c ac c d e f g h ah i j k l m n o p b²c q b²c r s t u v w bdv ab³c x y z A mp² b²c ab³c b²c ab³c ab³D B ac² C D ab³c b²c ab³c E ac² bc² ac² bc² b²c b³h b²c ab³c ac² bc² aci c²x abc²x b²c bc² b²c ab³c F G

Monoid Structure