Details Page for 0.7551

Complete Solution is Known:

MSV File: q-0.7551.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₄₀(0.7551):

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, b³⁴=b³², bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², b²f=b⁹, cf=ab⁹, df=ab¹¹, ef=ab¹³, f²=b¹⁴, b³g=ab¹¹, cg=ab²g, dg=b¹², eg=b¹⁴, fg=ab¹⁵, g²=b¹⁶, b⁴h=b¹³, ch=ab²h, dh=ab¹³, eh=ab¹⁵, fh=b¹⁶, gh=ab¹⁷, h²=b¹⁸, b⁵i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=b¹⁶, fi=ab¹⁷, gi=b¹⁸, hi=ab¹⁹, i²=b²⁰, b⁶j=b¹⁷, cj=ab²j, dj=ab⁴j, ej=ab¹⁷, fj=b¹⁸, gj=ab¹⁹, hj=b²⁰, ij=ab²¹, j²=b²², b⁷k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁶k, fk=ab¹⁹, gk=b²⁰, hk=ab²¹, ik=b²², jk=ab²³, k²=b²⁴, b⁸l=b²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=b⁷l, gl=ab²¹, hl=b²², il=ab²³, jl=b²⁴, kl=ab²⁵, l²=b²⁶, b⁹m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=b⁷m, gm=ab⁸m, hm=ab²³, im=b²⁴, jm=ab²⁵, km=b²⁶, lm=ab²⁷, m²=b²⁸, b¹⁰n=b²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=b⁷n, gn=ab⁸n, hn=b⁹n, in=ab²⁵, jn=b²⁶, kn=ab²⁷, ln=b²⁸, mn=ab²⁹, n²=b³⁰, b¹¹o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=b⁷o, go=ab⁸o, ho=b⁹o, io=ab¹⁰o, jo=ab²⁷, ko=b²⁸, lo=ab²⁹, mo=b³⁰, no=ab³¹, o²=b³², b¹²p=b²⁹, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=b⁷p, gp=ab⁸p, hp=b⁹p, ip=ab¹⁰p, jp=b¹¹p, kp=ab²⁹, lp=b³⁰, mp=ab³¹, np=b³², op=ab³³, p²=b³², b¹³q=ab³¹, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=b⁷q, gq=ab⁸q, hq=b⁹q, iq=ab¹⁰q, jq=b¹¹q, kq=ab¹²q, lq=ab³¹, mq=b³², nq=ab³³, oq=b³², pq=ab³³, q²=b³², b¹⁴r=b³³, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=b⁷r, gr=ab⁸r, hr=b⁹r, ir=ab¹⁰r, jr=b¹¹r, kr=ab¹²r, lr=b¹³r, mr=ab³³, nr=b³², or=ab³³, pr=b³², qr=ab³³, r²=b³², b¹⁴s=ab¹³r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=b⁷s, gs=ab⁸s, hs=b⁹s, is=ab¹⁰s, js=b¹¹s, ks=ab¹²s, ls=b¹³s, ms=b¹³r, ns=ab³³, os=b³², ps=ab³³, qs=b³², rs=ab³³, s²=b³², b¹³t=ab¹²s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=b⁷t, gt=ab⁸t, ht=b⁹t, it=ab¹⁰t, jt=b¹¹t, kt=ab¹²t, lt=ab¹²s, mt=b¹³s, nt=b¹³r, ot=ab³³, pt=b³², qt=ab³³, rt=b³², st=ab³³, t²=b³², b¹²u=ab¹¹t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=b⁷u, gu=ab⁸u, hu=b⁹u, iu=ab¹⁰u, ju=b¹¹u, ku=b¹¹t, lu=ab¹²t, mu=ab¹²s, nu=b¹³s, ou=b¹³r, pu=ab³³, qu=b³², ru=ab³³, su=b³², tu=ab³³, u²=b³², b¹¹v=ab¹⁰u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=b⁷v, gv=ab⁸v, hv=b⁹v, iv=ab¹⁰v, jv=ab¹⁰u, kv=b¹¹u, lv=b¹¹t, mv=ab¹²t, nv=ab¹²s, ov=b¹³s, pv=b¹³r, qv=ab³³, rv=b³², sv=ab³³, tv=b³², uv=ab³³, v²=b³², b¹⁰w=ab⁹v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=b⁷w, gw=ab⁸w, hw=b⁹w, iw=b⁹v, jw=ab¹⁰v, kw=ab¹⁰u, lw=b¹¹u, mw=b¹¹t, nw=ab¹²t, ow=ab¹²s, pw=b¹³s, qw=b¹³r, rw=ab³³, sw=b³², tw=ab³³, uw=b³², vw=ab³³, w²=b³², b⁹x=ab⁸w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=b⁷x, gx=ab⁸x, hx=ab⁸w, ix=b⁹w, jx=b⁹v, kx=ab¹⁰v, lx=ab¹⁰u, mx=b¹¹u, nx=b¹¹t, ox=ab¹²t, px=ab¹²s, qx=b¹³s, rx=b¹³r, sx=ab³³, tx=b³², ux=ab³³, vx=b³², wx=ab³³, x²=b³², b⁸y=ab⁷x, cy=ab²y, dy=ab⁴y, ey=ab⁶y, fy=b⁷y, gy=b⁷x, hy=ab⁸x, iy=ab⁸w, jy=b⁹w, ky=b⁹v, ly=ab¹⁰v, my=ab¹⁰u, ny=b¹¹u, oy=b¹¹t, py=ab¹²t, qy=ab¹²s, ry=b¹³s, sy=b¹³r, ty=ab³³, uy=b³², vy=ab³³, wy=b³², xy=ab³³, y²=b³², b⁷z=ab⁶y, cz=ab²z, dz=ab⁴z, ez=ab⁶z, fz=ab⁶y, gz=b⁷y, hz=b⁷x, iz=ab⁸x, jz=ab⁸w, kz=b⁹w, lz=b⁹v, mz=ab¹⁰v, nz=ab¹⁰u, oz=b¹¹u, pz=b¹¹t, qz=ab¹²t, rz=ab¹²s, sz=b¹³s, tz=b¹³r, uz=ab³³, vz=b³², wz=ab³³, xz=b³², yz=ab³³, z²=b³², b⁶A=ab⁵z, cA=ab²A, dA=ab⁴A, eA=b⁵z, fA=ab⁶z, gA=ab⁶y, hA=b⁷y, iA=b⁷x, jA=ab⁸x, kA=ab⁸w, lA=b⁹w, mA=b⁹v, nA=ab¹⁰v, oA=ab¹⁰u, pA=b¹¹u, qA=b¹¹t, rA=ab¹²t, sA=ab¹²s, tA=b¹³s, uA=b¹³r, vA=ab³³, wA=b³², xA=ab³³, yA=b³², zA=ab³³, A²=b³², b⁵B=ab⁴A, cB=ab²B, dB=ab⁴B, eB=b⁵A, fB=b⁵z, gB=ab⁶z, hB=ab⁶y, iB=b⁷y, jB=b⁷x, kB=ab⁸x, lB=ab⁸w, mB=b⁹w, nB=b⁹v, oB=ab¹⁰v, pB=ab¹⁰u, qB=b¹¹u, rB=b¹¹t, sB=ab¹²t, tB=ab¹²s, uB=b¹³s, vB=b¹³r, wB=ab³³, xB=b³², yB=ab³³, zB=b³², AB=ab³³, B²=b³², b⁴C=ab³B, cC=ab²C, dC=b³B, eC=ab⁴A, fC=b⁵A, gC=b⁵z, hC=ab⁶z, iC=ab⁶y, jC=b⁷y, kC=b⁷x, lC=ab⁸x, mC=ab⁸w, nC=b⁹w, oC=b⁹v, pC=ab¹⁰v, qC=ab¹⁰u, rC=b¹¹u, sC=b¹¹t, tC=ab¹²t, uC=ab¹²s, vC=b¹³s, wC=b¹³r, xC=ab³³, yC=b³², zC=ab³³, AC=b³², BC=ab³³, C²=b³², b³D=ab²C, cD=ab²D, dD=b³C, eD=ab⁴B, fD=ab⁴A, gD=b⁵A, hD=b⁵z, iD=ab⁶z, jD=ab⁶y, kD=b⁷y, lD=b⁷x, mD=ab⁸x, nD=ab⁸w, oD=b⁹w, pD=b⁹v, qD=ab¹⁰v, rD=ab¹⁰u, sD=b¹¹u, tD=b¹¹t, uD=ab¹²t, vD=ab¹²s, wD=b¹³s, xD=b¹³r, yD=ab³³, zD=b³², AD=ab³³, BD=b³², CD=ab³³, D²=b³², b²E=abD, cE=bD, dE=ab²C, eE=b³B, fE=ab⁴B, gE=ab⁴A, hE=b⁵A, iE=b⁵z, jE=ab⁶z, kE=ab⁶y, lE=b⁷y, mE=b⁷x, nE=ab⁸x, oE=ab⁸w, pE=b⁹w, qE=b⁹v, rE=ab¹⁰v, sE=ab¹⁰u, tE=b¹¹u, uE=b¹¹t, vE=ab¹²t, wE=ab¹²s, xE=b¹³s, yE=b¹³r, zE=ab³³, AE=b³², BE=ab³³, CE=b³², DE=ab³³, E²=b³², bF=aE, cF=bE, dF=ab²D, eF=b³C, fF=b³B, gF=ab⁴B, hF=ab⁴A, iF=b⁵A, jF=b⁵z, kF=ab⁶z, lF=ab⁶y, mF=b⁷y, nF=b⁷x, oF=ab⁸x, pF=ab⁸w, qF=b⁹w, rF=b⁹v, sF=ab¹⁰v, tF=ab¹⁰u, uF=b¹¹u, vF=b¹¹t, wF=ab¹²t, xF=ab¹²s, yF=b¹³s, zF=b¹³r, AF=ab³³, BF=b³², CF=ab³³, DF=b³², EF=ab³³, F²=b³², b⁴G=F, cG=ab²G, dG=aF, eG=bE, fG=bD, gG=ab²D, hG=ab²C, iG=b³C, jG=b³B, kG=ab⁴B, lG=ab⁴A, mG=b⁵A, nG=b⁵z, oG=ab⁶z, pG=ab⁶y, qG=b⁷y, rG=b⁷x, sG=ab⁸x, tG=ab⁸w, uG=b⁹w, vG=b⁹v, wG=ab¹⁰v, xG=ab¹⁰u, yG=b¹¹u, zG=b¹¹t, AG=ab¹²t, BG=ab¹²s, CG=b¹³s, DG=b¹³r, EG=ab³³, FG=b³², G²=b³²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, b³⁰, b³², af, bg, ah, ab²h, bi, b³i, aj, ab²j, ab⁴j, bk, b³k, b⁵k, al, ab²l, ab⁴l, ab⁶l, bm, b³m, b⁵m, b⁷m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, bo, b³o, b⁵o, b⁷o, b⁹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, bq, b³q, b⁵q, b⁷q, b⁹q, b¹¹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, ab¹⁰r, ab¹²r, bs, b³s, b⁵s, b⁷s, b⁹s, b¹¹s, b¹³s, at, ab²t, ab⁴t, ab⁶t, ab⁸t, ab¹⁰t, ab¹²t, bu, b³u, b⁵u, b⁷u, b⁹u, b¹¹u, av, ab²v, ab⁴v, ab⁶v, ab⁸v, ab¹⁰v, bw, b³w, b⁵w, b⁷w, b⁹w, ax, ab²x, ab⁴x, ab⁶x, ab⁸x, by, b³y, b⁵y, b⁷y, az, ab²z, ab⁴z, ab⁶z, bA, b³A, b⁵A, aB, ab²B, ab⁴B, bC, b³C, aD, ab²D, bE, aF, aG, ab²G}

Phi = 1 a b a b c b³ d b⁵ 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 ab³G b²G abG G

Monoid Structure