Details Page for 0.1751

Complete Solution is Known:

MSV File: q-0.1751.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₆(0.1751):

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 | a²=1, b²⁹=b²⁷, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b³f=ab⁹, cf=ab²f, df=b¹⁰, ef=ab¹¹, f²=b¹², b⁴g=b¹¹, cg=ab²g, dg=ab¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=ab¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=b¹⁵, ci=ab²i, di=ab⁴i, ei=b⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b²⁰, b⁸k=b¹⁹, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁶k, gk=b⁷k, hk=ab¹⁹, ik=b²⁰, jk=ab²¹, k²=b²², b⁹l=ab²¹, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁶l, gl=b⁷l, hl=ab⁸l, il=ab²¹, jl=b²², kl=ab²³, l²=b²⁴, b¹⁰m=b²³, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁶m, gm=b⁷m, hm=ab⁸m, im=b⁹m, jm=ab²³, km=b²⁴, lm=ab²⁵, m²=b²⁶, b¹¹n=ab²⁵, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁶n, gn=b⁷n, hn=ab⁸n, in=b⁹n, jn=ab¹⁰n, kn=ab²⁵, ln=b²⁶, mn=ab²⁷, n²=b²⁸, b¹²o=b²⁷, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁶o, go=b⁷o, ho=ab⁸o, io=b⁹o, jo=ab¹⁰o, ko=b¹¹o, lo=ab²⁷, mo=b²⁸, no=ab²⁷, o²=b²⁸, b¹³p=ab²⁷, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁶p, gp=b⁷p, hp=ab⁸p, ip=b⁹p, jp=ab¹⁰p, kp=b¹¹p, lp=ab¹²p, mp=ab²⁷, np=b²⁸, op=ab²⁷, p²=b²⁸, b¹²q=ab¹¹p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁶q, gq=b⁷q, hq=ab⁸q, iq=b⁹q, jq=ab¹⁰q, kq=b¹¹q, lq=b¹¹p, mq=ab¹²p, nq=ab²⁷, oq=b²⁸, pq=ab²⁷, q²=b²⁸, b¹¹r=ab¹⁰q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁶r, gr=b⁷r, hr=ab⁸r, ir=b⁹r, jr=ab¹⁰r, kr=ab¹⁰q, lr=b¹¹q, mr=b¹¹p, nr=ab¹²p, or=ab²⁷, pr=b²⁸, qr=ab²⁷, r²=b²⁸, b¹⁰s=ab⁹r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁶s, gs=b⁷s, hs=ab⁸s, is=b⁹s, js=b⁹r, ks=ab¹⁰r, ls=ab¹⁰q, ms=b¹¹q, ns=b¹¹p, os=ab¹²p, ps=ab²⁷, qs=b²⁸, rs=ab²⁷, s²=b²⁸, b⁹t=ab⁸s, ct=ab²t, dt=ab⁴t, et=b⁵t, ft=ab⁶t, gt=b⁷t, ht=ab⁸t, it=ab⁸s, jt=b⁹s, kt=b⁹r, lt=ab¹⁰r, mt=ab¹⁰q, nt=b¹¹q, ot=b¹¹p, pt=ab¹²p, qt=ab²⁷, rt=b²⁸, st=ab²⁷, t²=b²⁸, b⁸u=ab⁷t, cu=ab²u, du=ab⁴u, eu=b⁵u, fu=ab⁶u, gu=b⁷u, hu=b⁷t, iu=ab⁸t, ju=ab⁸s, ku=b⁹s, lu=b⁹r, mu=ab¹⁰r, nu=ab¹⁰q, ou=b¹¹q, pu=b¹¹p, qu=ab¹²p, ru=ab²⁷, su=b²⁸, tu=ab²⁷, u²=b²⁸, b⁷v=ab⁶u, cv=ab²v, dv=ab⁴v, ev=b⁵v, fv=ab⁶v, gv=ab⁶u, hv=b⁷u, iv=b⁷t, jv=ab⁸t, kv=ab⁸s, lv=b⁹s, mv=b⁹r, nv=ab¹⁰r, ov=ab¹⁰q, pv=b¹¹q, qv=b¹¹p, rv=ab¹²p, sv=ab²⁷, tv=b²⁸, uv=ab²⁷, v²=b²⁸, b⁶w=ab⁵v, cw=ab²w, dw=ab⁴w, ew=b⁵w, fw=b⁵v, gw=ab⁶v, hw=ab⁶u, iw=b⁷u, jw=b⁷t, kw=ab⁸t, lw=ab⁸s, mw=b⁹s, nw=b⁹r, ow=ab¹⁰r, pw=ab¹⁰q, qw=b¹¹q, rw=b¹¹p, sw=ab¹²p, tw=ab²⁷, uw=b²⁸, vw=ab²⁷, w²=b²⁸, b⁵x=ab⁴w, cx=ab²x, dx=ab⁴x, ex=ab⁴w, fx=b⁵w, gx=b⁵v, hx=ab⁶v, ix=ab⁶u, jx=b⁷u, kx=b⁷t, lx=ab⁸t, mx=ab⁸s, nx=b⁹s, ox=b⁹r, px=ab¹⁰r, qx=ab¹⁰q, rx=b¹¹q, sx=b¹¹p, tx=ab¹²p, ux=ab²⁷, vx=b²⁸, wx=ab²⁷, x²=b²⁸, b⁴y=ab³x, cy=ab²y, dy=b³x, ey=ab⁴x, fy=ab⁴w, gy=b⁵w, hy=b⁵v, iy=ab⁶v, jy=ab⁶u, ky=b⁷u, ly=b⁷t, my=ab⁸t, ny=ab⁸s, oy=b⁹s, py=b⁹r, qy=ab¹⁰r, ry=ab¹⁰q, sy=b¹¹q, ty=b¹¹p, uy=ab¹²p, vy=ab²⁷, wy=b²⁸, xy=ab²⁷, y²=b²⁸, b³z=ab²y, cz=ab²z, dz=b³y, ez=b³x, fz=ab⁴x, gz=ab⁴w, hz=b⁵w, iz=b⁵v, jz=ab⁶v, kz=ab⁶u, lz=b⁷u, mz=b⁷t, nz=ab⁸t, oz=ab⁸s, pz=b⁹s, qz=b⁹r, rz=ab¹⁰r, sz=ab¹⁰q, tz=b¹¹q, uz=b¹¹p, vz=ab¹²p, wz=ab²⁷, xz=b²⁸, yz=ab²⁷, z²=b²⁸, b²A=abz, cA=bz, dA=ab²y, eA=b³y, fA=b³x, gA=ab⁴x, hA=ab⁴w, iA=b⁵w, jA=b⁵v, kA=ab⁶v, lA=ab⁶u, mA=b⁷u, nA=b⁷t, oA=ab⁸t, pA=ab⁸s, qA=b⁹s, rA=b⁹r, sA=ab¹⁰r, tA=ab¹⁰q, uA=b¹¹q, vA=b¹¹p, wA=ab¹²p, xA=ab²⁷, yA=b²⁸, zA=ab²⁷, A²=b²⁸, bB=aA, cB=bA, dB=ab²z, eB=ab²y, fB=b³y, gB=b³x, hB=ab⁴x, iB=ab⁴w, jB=b⁵w, kB=b⁵v, lB=ab⁶v, mB=ab⁶u, nB=b⁷u, oB=b⁷t, pB=ab⁸t, qB=ab⁸s, rB=b⁹s, sB=b⁹r, tB=ab¹⁰r, uB=ab¹⁰q, vB=b¹¹q, wB=b¹¹p, xB=ab¹²p, yB=ab²⁷, zB=b²⁸, AB=ab²⁷, B²=b²⁸, bC=aB, cC=aA, dC=bz, eC=ab²z, fC=ab²y, gC=b³y, hC=b³x, iC=ab⁴x, jC=ab⁴w, kC=b⁵w, lC=b⁵v, mC=ab⁶v, nC=ab⁶u, oC=b⁷u, pC=b⁷t, qC=ab⁸t, rC=ab⁸s, sC=b⁹s, tC=b⁹r, uC=ab¹⁰r, vC=ab¹⁰q, wC=b¹¹q, xC=b¹¹p, yC=ab¹²p, zC=ab²⁷, AC=b²⁸, BC=ab²⁷, C²=b²⁸, bD=aC, cD=aB, dD=bA, eD=bz, fD=ab²z, gD=ab²y, hD=b³y, iD=b³x, jD=ab⁴x, kD=ab⁴w, lD=b⁵w, mD=b⁵v, nD=ab⁶v, oD=ab⁶u, pD=b⁷u, qD=b⁷t, rD=ab⁸t, sD=ab⁸s, tD=b⁹s, uD=b⁹r, vD=ab¹⁰r, wD=ab¹⁰q, xD=b¹¹q, yD=b¹¹p, zD=ab¹²p, AD=ab²⁷, BD=b²⁸, CD=ab²⁷, D²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, ae, bf, ag, ab²g, bh, b³h, ai, ab²i, ab⁴i, bj, b³j, b⁵j, ak, ab²k, ab⁴k, ab⁶k, bl, b³l, b⁵l, b⁷l, am, ab²m, ab⁴m, ab⁶m, ab⁸m, bn, b³n, b⁵n, b⁷n, b⁹n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, ab¹⁰o, bp, b³p, b⁵p, b⁷p, b⁹p, b¹¹p, aq, ab²q, ab⁴q, ab⁶q, ab⁸q, ab¹⁰q, br, b³r, b⁵r, b⁷r, b⁹r, as, ab²s, ab⁴s, ab⁶s, ab⁸s, bt, b³t, b⁵t, b⁷t, au, ab²u, ab⁴u, ab⁶u, bv, b³v, b⁵v, aw, ab²w, ab⁴w, bx, b³x, ay, ab²y, bz, aA, aC}

Phi = 1 a a b b a a b b c c b³ b³ d d b⁵ e ab⁶ f b⁷ g ab⁸ h b⁹ i ab¹⁰ j b¹¹ k ab¹² l b¹³ m ab¹⁴ n b¹⁵ o ab¹⁶ p b¹⁷ q ab¹⁸ r b¹⁹ s ab²⁰ t b²¹ u ab²² v b²³ w ab²⁴ x b²⁵ y ab²⁶ z b²⁷ A ab²⁸ B b²⁷ C ab²⁸ D b²⁷

Monoid Structure