Details Page for 0.7541

Complete Solution is Known:

MSV File: q-0.7541.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₉(0.7541):

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, b³³=b³¹, 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=ab³¹, 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=ab³¹, oq=b³², pq=ab³¹, q²=b³², b¹⁴r=b³¹, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=b⁷r, gr=ab⁸r, hr=b⁹r, ir=ab¹⁰r, jr=b¹¹r, kr=ab¹²r, lr=b¹³r, mr=ab³¹, nr=b³², or=ab³¹, pr=b³², qr=ab³¹, r²=b³², b¹³s=ab¹²r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=b⁷s, gs=ab⁸s, hs=b⁹s, is=ab¹⁰s, js=b¹¹s, ks=ab¹²s, ls=ab¹²r, ms=b¹³r, ns=ab³¹, os=b³², ps=ab³¹, qs=b³², rs=ab³¹, s²=b³², b¹²t=ab¹¹s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=b⁷t, gt=ab⁸t, ht=b⁹t, it=ab¹⁰t, jt=b¹¹t, kt=b¹¹s, lt=ab¹²s, mt=ab¹²r, nt=b¹³r, ot=ab³¹, pt=b³², qt=ab³¹, rt=b³², st=ab³¹, t²=b³², b¹¹u=ab¹⁰t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=b⁷u, gu=ab⁸u, hu=b⁹u, iu=ab¹⁰u, ju=ab¹⁰t, ku=b¹¹t, lu=b¹¹s, mu=ab¹²s, nu=ab¹²r, ou=b¹³r, pu=ab³¹, qu=b³², ru=ab³¹, su=b³², tu=ab³¹, u²=b³², b¹⁰v=ab⁹u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=b⁷v, gv=ab⁸v, hv=b⁹v, iv=b⁹u, jv=ab¹⁰u, kv=ab¹⁰t, lv=b¹¹t, mv=b¹¹s, nv=ab¹²s, ov=ab¹²r, pv=b¹³r, qv=ab³¹, rv=b³², sv=ab³¹, tv=b³², uv=ab³¹, v²=b³², b⁹w=ab⁸v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=b⁷w, gw=ab⁸w, hw=ab⁸v, iw=b⁹v, jw=b⁹u, kw=ab¹⁰u, lw=ab¹⁰t, mw=b¹¹t, nw=b¹¹s, ow=ab¹²s, pw=ab¹²r, qw=b¹³r, rw=ab³¹, sw=b³², tw=ab³¹, uw=b³², vw=ab³¹, w²=b³², b⁸x=ab⁷w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=b⁷x, gx=b⁷w, hx=ab⁸w, ix=ab⁸v, jx=b⁹v, kx=b⁹u, lx=ab¹⁰u, mx=ab¹⁰t, nx=b¹¹t, ox=b¹¹s, px=ab¹²s, qx=ab¹²r, rx=b¹³r, sx=ab³¹, tx=b³², ux=ab³¹, vx=b³², wx=ab³¹, x²=b³², b⁷y=ab⁶x, cy=ab²y, dy=ab⁴y, ey=ab⁶y, fy=ab⁶x, gy=b⁷x, hy=b⁷w, iy=ab⁸w, jy=ab⁸v, ky=b⁹v, ly=b⁹u, my=ab¹⁰u, ny=ab¹⁰t, oy=b¹¹t, py=b¹¹s, qy=ab¹²s, ry=ab¹²r, sy=b¹³r, ty=ab³¹, uy=b³², vy=ab³¹, wy=b³², xy=ab³¹, y²=b³², b⁶z=ab⁵y, cz=ab²z, dz=ab⁴z, ez=b⁵y, fz=ab⁶y, gz=ab⁶x, hz=b⁷x, iz=b⁷w, jz=ab⁸w, kz=ab⁸v, lz=b⁹v, mz=b⁹u, nz=ab¹⁰u, oz=ab¹⁰t, pz=b¹¹t, qz=b¹¹s, rz=ab¹²s, sz=ab¹²r, tz=b¹³r, uz=ab³¹, vz=b³², wz=ab³¹, xz=b³², yz=ab³¹, z²=b³², b⁵A=ab⁴z, cA=ab²A, dA=ab⁴A, eA=b⁵z, fA=b⁵y, gA=ab⁶y, hA=ab⁶x, iA=b⁷x, jA=b⁷w, kA=ab⁸w, lA=ab⁸v, mA=b⁹v, nA=b⁹u, oA=ab¹⁰u, pA=ab¹⁰t, qA=b¹¹t, rA=b¹¹s, sA=ab¹²s, tA=ab¹²r, uA=b¹³r, vA=ab³¹, wA=b³², xA=ab³¹, yA=b³², zA=ab³¹, A²=b³², b⁴B=ab³A, cB=ab²B, dB=b³A, eB=ab⁴z, fB=b⁵z, gB=b⁵y, hB=ab⁶y, iB=ab⁶x, jB=b⁷x, kB=b⁷w, lB=ab⁸w, mB=ab⁸v, nB=b⁹v, oB=b⁹u, pB=ab¹⁰u, qB=ab¹⁰t, rB=b¹¹t, sB=b¹¹s, tB=ab¹²s, uB=ab¹²r, vB=b¹³r, wB=ab³¹, xB=b³², yB=ab³¹, zB=b³², AB=ab³¹, B²=b³², b³C=ab²B, cC=ab²C, dC=b³B, eC=ab⁴A, fC=ab⁴z, gC=b⁵z, hC=b⁵y, iC=ab⁶y, jC=ab⁶x, kC=b⁷x, lC=b⁷w, mC=ab⁸w, nC=ab⁸v, oC=b⁹v, pC=b⁹u, qC=ab¹⁰u, rC=ab¹⁰t, sC=b¹¹t, tC=b¹¹s, uC=ab¹²s, vC=ab¹²r, wC=b¹³r, xC=ab³¹, yC=b³², zC=ab³¹, AC=b³², BC=ab³¹, C²=b³², b²D=abC, cD=bC, dD=ab²B, eD=b³A, fD=ab⁴A, gD=ab⁴z, hD=b⁵z, iD=b⁵y, jD=ab⁶y, kD=ab⁶x, lD=b⁷x, mD=b⁷w, nD=ab⁸w, oD=ab⁸v, pD=b⁹v, qD=b⁹u, rD=ab¹⁰u, sD=ab¹⁰t, tD=b¹¹t, uD=b¹¹s, vD=ab¹²s, wD=ab¹²r, xD=b¹³r, yD=ab³¹, zD=b³², AD=ab³¹, BD=b³², CD=ab³¹, D²=b³², bE=aD, cE=bD, dE=ab²C, eE=b³B, fE=b³A, gE=ab⁴A, hE=ab⁴z, iE=b⁵z, jE=b⁵y, kE=ab⁶y, lE=ab⁶x, mE=b⁷x, nE=b⁷w, oE=ab⁸w, pE=ab⁸v, qE=b⁹v, rE=b⁹u, sE=ab¹⁰u, tE=ab¹⁰t, uE=b¹¹t, vE=b¹¹s, wE=ab¹²s, xE=ab¹²r, yE=b¹³r, zE=ab³¹, AE=b³², BE=ab³¹, CE=b³², DE=ab³¹, E²=b³², bF=aE, cF=aD, dF=bC, eF=ab²B, fF=b³B, gF=b³A, hF=ab⁴A, iF=ab⁴z, jF=b⁵z, kF=b⁵y, lF=ab⁶y, mF=ab⁶x, nF=b⁷x, oF=b⁷w, pF=ab⁸w, qF=ab⁸v, rF=b⁹v, sF=b⁹u, tF=ab¹⁰u, uF=ab¹⁰t, vF=b¹¹t, wF=b¹¹s, xF=ab¹²s, yF=ab¹²r, zF=b¹³r, AF=ab³¹, BF=b³², CF=ab³¹, DF=b³², EF=ab³¹, F²=b³², b³G=aF, cG=ab²G, dG=aE, eG=bD, fG=bC, gG=ab²C, hG=ab²B, iG=b³B, jG=b³A, kG=ab⁴A, lG=ab⁴z, mG=b⁵z, nG=b⁵y, oG=ab⁶y, pG=ab⁶x, qG=b⁷x, rG=b⁷w, sG=ab⁸w, tG=ab⁸v, uG=b⁹v, vG=b⁹u, wG=ab¹⁰u, xG=ab¹⁰t, yG=b¹¹t, zG=b¹¹s, AG=ab¹²s, BG=ab¹²r, CG=b¹³r, DG=ab³¹, EG=b³², FG=ab³¹, 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, at, ab²t, ab⁴t, ab⁶t, ab⁸t, ab¹⁰t, bu, b³u, b⁵u, b⁷u, b⁹u, av, ab²v, ab⁴v, ab⁶v, ab⁸v, bw, b³w, b⁵w, b⁷w, ax, ab²x, ab⁴x, ab⁶x, by, b³y, b⁵y, az, ab²z, ab⁴z, bA, b³A, aB, ab²B, bC, aD, aF, bG}

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 b²G abG G

Monoid Structure