Details Page for 0.3551

Complete Solution is Known:

MSV File: q-0.3551.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₄₇(0.3551):

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, b³⁷=b³⁵, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², bf=ab⁹, cf=b¹⁰, df=b¹², ef=b¹⁴, f²=b¹⁶, b²g=b¹¹, cg=ab¹¹, dg=ab¹³, eg=ab¹⁵, fg=ab¹⁷, g²=b¹⁸, b³h=ab¹³, ch=ab²h, dh=b¹⁴, eh=b¹⁶, fh=b¹⁸, gh=ab¹⁹, h²=b²⁰, b⁴i=b¹⁵, ci=ab²i, di=ab¹⁵, ei=ab¹⁷, fi=ab¹⁹, gi=b²⁰, hi=ab²¹, i²=b²², b⁵j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b¹⁸, fj=b²⁰, gj=ab²¹, hj=b²², ij=ab²³, j²=b²⁴, b⁶k=b¹⁹, ck=ab²k, dk=ab⁴k, ek=ab¹⁹, fk=ab²¹, gk=b²², hk=ab²³, ik=b²⁴, jk=ab²⁵, k²=b²⁶, b⁷l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=b²², gl=ab²³, hl=b²⁴, il=ab²⁵, jl=b²⁶, kl=ab²⁷, l²=b²⁸, b⁸m=b²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=ab²³, gm=b²⁴, hm=ab²⁵, im=b²⁶, jm=ab²⁷, km=b²⁸, lm=ab²⁹, m²=b³⁰, b⁹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=ab⁸n, gn=ab²⁵, hn=b²⁶, in=ab²⁷, jn=b²⁸, kn=ab²⁹, ln=b³⁰, mn=ab³¹, n²=b³², b¹⁰o=b²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=ab⁸o, go=b⁹o, ho=ab²⁷, io=b²⁸, jo=ab²⁹, ko=b³⁰, lo=ab³¹, mo=b³², no=ab³³, o²=b³⁴, b¹¹p=ab²⁹, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=ab⁸p, gp=b⁹p, hp=ab¹⁰p, ip=ab²⁹, jp=b³⁰, kp=ab³¹, lp=b³², mp=ab³³, np=b³⁴, op=ab³⁵, p²=b³⁶, b¹²q=b³¹, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁸q, gq=b⁹q, hq=ab¹⁰q, iq=b¹¹q, jq=ab³¹, kq=b³², lq=ab³³, mq=b³⁴, nq=ab³⁵, oq=b³⁶, pq=ab³⁵, q²=b³⁶, b¹³r=ab³³, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=ab⁸r, gr=b⁹r, hr=ab¹⁰r, ir=b¹¹r, jr=ab¹²r, kr=ab³³, lr=b³⁴, mr=ab³⁵, nr=b³⁶, or=ab³⁵, pr=b³⁶, qr=ab³⁵, r²=b³⁶, b¹⁴s=b³⁵, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁸s, gs=b⁹s, hs=ab¹⁰s, is=b¹¹s, js=ab¹²s, ks=b¹³s, ls=ab³⁵, ms=b³⁶, ns=ab³⁵, os=b³⁶, ps=ab³⁵, qs=b³⁶, rs=ab³⁵, s²=b³⁶, b¹⁵t=ab³⁵, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=ab⁸t, gt=b⁹t, ht=ab¹⁰t, it=b¹¹t, jt=ab¹²t, kt=b¹³t, lt=ab¹⁴t, mt=ab³⁵, nt=b³⁶, ot=ab³⁵, pt=b³⁶, qt=ab³⁵, rt=b³⁶, st=ab³⁵, t²=b³⁶, b¹⁴u=ab¹³t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=ab⁸u, gu=b⁹u, hu=ab¹⁰u, iu=b¹¹u, ju=ab¹²u, ku=b¹³u, lu=b¹³t, mu=ab¹⁴t, nu=ab³⁵, ou=b³⁶, pu=ab³⁵, qu=b³⁶, ru=ab³⁵, su=b³⁶, tu=ab³⁵, u²=b³⁶, b¹³v=ab¹²u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=ab⁸v, gv=b⁹v, hv=ab¹⁰v, iv=b¹¹v, jv=ab¹²v, kv=ab¹²u, lv=b¹³u, mv=b¹³t, nv=ab¹⁴t, ov=ab³⁵, pv=b³⁶, qv=ab³⁵, rv=b³⁶, sv=ab³⁵, tv=b³⁶, uv=ab³⁵, v²=b³⁶, b¹²w=ab¹¹v, cw=ab²w, dw=ab⁴w, ew=ab⁶w, fw=ab⁸w, gw=b⁹w, hw=ab¹⁰w, iw=b¹¹w, jw=b¹¹v, kw=ab¹²v, lw=ab¹²u, mw=b¹³u, nw=b¹³t, ow=ab¹⁴t, pw=ab³⁵, qw=b³⁶, rw=ab³⁵, sw=b³⁶, tw=ab³⁵, uw=b³⁶, vw=ab³⁵, w²=b³⁶, b¹¹x=ab¹⁰w, cx=ab²x, dx=ab⁴x, ex=ab⁶x, fx=ab⁸x, gx=b⁹x, hx=ab¹⁰x, ix=ab¹⁰w, jx=b¹¹w, kx=b¹¹v, lx=ab¹²v, mx=ab¹²u, nx=b¹³u, ox=b¹³t, px=ab¹⁴t, qx=ab³⁵, rx=b³⁶, sx=ab³⁵, tx=b³⁶, ux=ab³⁵, vx=b³⁶, wx=ab³⁵, x²=b³⁶, b¹⁰y=ab⁹x, cy=ab²y, dy=ab⁴y, ey=ab⁶y, fy=ab⁸y, gy=b⁹y, hy=b⁹x, iy=ab¹⁰x, jy=ab¹⁰w, ky=b¹¹w, ly=b¹¹v, my=ab¹²v, ny=ab¹²u, oy=b¹³u, py=b¹³t, qy=ab¹⁴t, ry=ab³⁵, sy=b³⁶, ty=ab³⁵, uy=b³⁶, vy=ab³⁵, wy=b³⁶, xy=ab³⁵, y²=b³⁶, b⁹z=ab⁸y, cz=ab²z, dz=ab⁴z, ez=ab⁶z, fz=ab⁸z, gz=ab⁸y, hz=b⁹y, iz=b⁹x, jz=ab¹⁰x, kz=ab¹⁰w, lz=b¹¹w, mz=b¹¹v, nz=ab¹²v, oz=ab¹²u, pz=b¹³u, qz=b¹³t, rz=ab¹⁴t, sz=ab³⁵, tz=b³⁶, uz=ab³⁵, vz=b³⁶, wz=ab³⁵, xz=b³⁶, yz=ab³⁵, z²=b³⁶, b⁸A=ab⁷z, cA=ab²A, dA=ab⁴A, eA=ab⁶A, fA=b⁷z, gA=ab⁸z, hA=ab⁸y, iA=b⁹y, jA=b⁹x, kA=ab¹⁰x, lA=ab¹⁰w, mA=b¹¹w, nA=b¹¹v, oA=ab¹²v, pA=ab¹²u, qA=b¹³u, rA=b¹³t, sA=ab¹⁴t, tA=ab³⁵, uA=b³⁶, vA=ab³⁵, wA=b³⁶, xA=ab³⁵, yA=b³⁶, zA=ab³⁵, A²=b³⁶, b⁷B=ab⁶A, cB=ab²B, dB=ab⁴B, eB=ab⁶B, fB=b⁷A, gB=b⁷z, hB=ab⁸z, iB=ab⁸y, jB=b⁹y, kB=b⁹x, lB=ab¹⁰x, mB=ab¹⁰w, nB=b¹¹w, oB=b¹¹v, pB=ab¹²v, qB=ab¹²u, rB=b¹³u, sB=b¹³t, tB=ab¹⁴t, uB=ab³⁵, vB=b³⁶, wB=ab³⁵, xB=b³⁶, yB=ab³⁵, zB=b³⁶, AB=ab³⁵, B²=b³⁶, b⁶C=ab⁵B, cC=ab²C, dC=ab⁴C, eC=b⁵B, fC=ab⁶A, gC=b⁷A, hC=b⁷z, iC=ab⁸z, jC=ab⁸y, kC=b⁹y, lC=b⁹x, mC=ab¹⁰x, nC=ab¹⁰w, oC=b¹¹w, pC=b¹¹v, qC=ab¹²v, rC=ab¹²u, sC=b¹³u, tC=b¹³t, uC=ab¹⁴t, vC=ab³⁵, wC=b³⁶, xC=ab³⁵, yC=b³⁶, zC=ab³⁵, AC=b³⁶, BC=ab³⁵, C²=b³⁶, b⁵D=ab⁴C, cD=ab²D, dD=ab⁴D, eD=b⁵C, fD=ab⁶B, gD=ab⁶A, hD=b⁷A, iD=b⁷z, jD=ab⁸z, kD=ab⁸y, lD=b⁹y, mD=b⁹x, nD=ab¹⁰x, oD=ab¹⁰w, pD=b¹¹w, qD=b¹¹v, rD=ab¹²v, sD=ab¹²u, tD=b¹³u, uD=b¹³t, vD=ab¹⁴t, wD=ab³⁵, xD=b³⁶, yD=ab³⁵, zD=b³⁶, AD=ab³⁵, BD=b³⁶, CD=ab³⁵, D²=b³⁶, b⁴E=ab³D, cE=ab²E, dE=b³D, eE=ab⁴C, fE=b⁵B, gE=ab⁶B, hE=ab⁶A, iE=b⁷A, jE=b⁷z, kE=ab⁸z, lE=ab⁸y, mE=b⁹y, nE=b⁹x, oE=ab¹⁰x, pE=ab¹⁰w, qE=b¹¹w, rE=b¹¹v, sE=ab¹²v, tE=ab¹²u, uE=b¹³u, vE=b¹³t, wE=ab¹⁴t, xE=ab³⁵, yE=b³⁶, zE=ab³⁵, AE=b³⁶, BE=ab³⁵, CE=b³⁶, DE=ab³⁵, E²=b³⁶, b³F=ab²E, cF=ab²F, dF=b³E, eF=ab⁴D, fF=b⁵C, gF=b⁵B, hF=ab⁶B, iF=ab⁶A, jF=b⁷A, kF=b⁷z, lF=ab⁸z, mF=ab⁸y, nF=b⁹y, oF=b⁹x, pF=ab¹⁰x, qF=ab¹⁰w, rF=b¹¹w, sF=b¹¹v, tF=ab¹²v, uF=ab¹²u, vF=b¹³u, wF=b¹³t, xF=ab¹⁴t, yF=ab³⁵, zF=b³⁶, AF=ab³⁵, BF=b³⁶, CF=ab³⁵, DF=b³⁶, EF=ab³⁵, F²=b³⁶, b⁹G=bF, cG=ab²G, dG=ab⁴G, eG=ab⁶G, fG=ab⁸G, gG=bF, hG=ab²F, iG=ab²E, jG=b³E, kG=b³D, lG=ab⁴D, mG=ab⁴C, nG=b⁵C, oG=b⁵B, pG=ab⁶B, qG=ab⁶A, rG=b⁷A, sG=b⁷z, tG=ab⁸z, uG=ab⁸y, vG=b⁹y, wG=b⁹x, xG=ab¹⁰x, yG=ab¹⁰w, zG=b¹¹w, AG=b¹¹v, BG=ab¹²v, CG=ab¹²u, DG=b¹³u, EG=b¹³t, FG=ab¹⁴t, G²=b³⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, b³⁰, b³², b³⁴, b³⁶, ag, bh, ai, ab²i, bj, b³j, ak, ab²k, ab⁴k, bl, b³l, b⁵l, am, ab²m, ab⁴m, ab⁶m, bn, b³n, b⁵n, b⁷n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, bp, b³p, b⁵p, b⁷p, b⁹p, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, ab¹⁰q, br, b³r, b⁵r, b⁷r, b⁹r, b¹¹r, as, ab²s, ab⁴s, ab⁶s, ab⁸s, ab¹⁰s, ab¹²s, bt, b³t, b⁵t, b⁷t, b⁹t, b¹¹t, b¹³t, au, ab²u, ab⁴u, ab⁶u, ab⁸u, ab¹⁰u, ab¹²u, bv, b³v, b⁵v, b⁷v, b⁹v, b¹¹v, aw, ab²w, ab⁴w, ab⁶w, ab⁸w, ab¹⁰w, bx, b³x, b⁵x, b⁷x, b⁹x, ay, ab²y, ab⁴y, ab⁶y, ab⁸y, bz, b³z, b⁵z, b⁷z, aA, ab²A, ab⁴A, ab⁶A, bB, b³B, b⁵B, aC, ab²C, ab⁴C, bD, b³D, aE, ab²E, bF, bG, b³G, b⁵G, b⁷G}

Phi = 1 a b a b a b c b³ d b⁵ e b⁷ 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 ab⁷G b⁶G ab⁵G b⁴G ab³G b²G abG G

Monoid Structure