Details Page for 0.7153

Complete Solution is Known:

MSV File: q-0.7153.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₀₅(0.7153):

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 | a²=1, b²⁷=b²⁵, bc=ab³, c²=b⁴, b²d=ab⁵, cd=b⁵, d²=b⁶, b³e=ab⁷, ce=ab²e, de=b⁷, e²=b⁸, b⁴f=ab⁹, cf=ab²f, df=ab³f, ef=b⁹, f²=b¹⁰, b⁵g=ab¹¹, cg=ab²g, dg=ab³g, eg=ab⁴g, fg=b¹¹, g²=b¹², b⁶h=ab¹³, ch=ab²h, dh=ab³h, eh=ab⁴h, fh=ab⁵h, gh=b¹³, h²=b¹⁴, b⁷i=ab¹⁵, ci=ab²i, di=ab³i, ei=ab⁴i, fi=ab⁵i, gi=ab⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=ab¹⁷, cj=ab²j, dj=ab³j, ej=ab⁴j, fj=ab⁵j, gj=ab⁶j, hj=ab⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=ab¹⁹, ck=ab²k, dk=ab³k, ek=ab⁴k, fk=ab⁵k, gk=ab⁶k, hk=ab⁷k, ik=ab⁸k, jk=b¹⁹, k²=b²⁰, b¹⁰l=ab²¹, cl=ab²l, dl=ab³l, el=ab⁴l, fl=ab⁵l, gl=ab⁶l, hl=ab⁷l, il=ab⁸l, jl=ab⁹l, kl=b²¹, l²=b²², b¹¹m=ab²³, cm=ab²m, dm=ab³m, em=ab⁴m, fm=ab⁵m, gm=ab⁶m, hm=ab⁷m, im=ab⁸m, jm=ab⁹m, km=ab¹⁰m, lm=b²³, m²=b²⁴, b¹²n=ab²⁵, cn=ab²n, dn=ab³n, en=ab⁴n, fn=ab⁵n, gn=ab⁶n, hn=ab⁷n, in=ab⁸n, jn=ab⁹n, kn=ab¹⁰n, ln=ab¹¹n, mn=b²⁵, n²=b²⁶, b¹³o=ab²⁵, co=ab²o, do=ab³o, eo=ab⁴o, fo=ab⁵o, go=ab⁶o, ho=ab⁷o, io=ab⁸o, jo=ab⁹o, ko=ab¹⁰o, lo=ab¹¹o, mo=ab¹²o, no=b²⁵, o²=b²⁶, b¹²p=b¹¹o, cp=ab²p, dp=ab³p, ep=ab⁴p, fp=ab⁵p, gp=ab⁶p, hp=ab⁷p, ip=ab⁸p, jp=ab⁹p, kp=ab¹⁰p, lp=ab¹¹p, mp=ab¹¹o, np=ab¹²o, op=b²⁵, p²=b²⁶, b¹¹q=b¹⁰p, cq=ab²q, dq=ab³q, eq=ab⁴q, fq=ab⁵q, gq=ab⁶q, hq=ab⁷q, iq=ab⁸q, jq=ab⁹q, kq=ab¹⁰q, lq=ab¹⁰p, mq=ab¹¹p, nq=ab¹¹o, oq=ab¹²o, pq=b²⁵, q²=b²⁶, b¹⁰r=b⁹q, cr=ab²r, dr=ab³r, er=ab⁴r, fr=ab⁵r, gr=ab⁶r, hr=ab⁷r, ir=ab⁸r, jr=ab⁹r, kr=ab⁹q, lr=ab¹⁰q, mr=ab¹⁰p, nr=ab¹¹p, or=ab¹¹o, pr=ab¹²o, qr=b²⁵, r²=b²⁶, b⁹s=b⁸r, cs=ab²s, ds=ab³s, es=ab⁴s, fs=ab⁵s, gs=ab⁶s, hs=ab⁷s, is=ab⁸s, js=ab⁸r, ks=ab⁹r, ls=ab⁹q, ms=ab¹⁰q, ns=ab¹⁰p, os=ab¹¹p, ps=ab¹¹o, qs=ab¹²o, rs=b²⁵, s²=b²⁶, b⁸t=b⁷s, ct=ab²t, dt=ab³t, et=ab⁴t, ft=ab⁵t, gt=ab⁶t, ht=ab⁷t, it=ab⁷s, jt=ab⁸s, kt=ab⁸r, lt=ab⁹r, mt=ab⁹q, nt=ab¹⁰q, ot=ab¹⁰p, pt=ab¹¹p, qt=ab¹¹o, rt=ab¹²o, st=b²⁵, t²=b²⁶, b⁷u=b⁶t, cu=ab²u, du=ab³u, eu=ab⁴u, fu=ab⁵u, gu=ab⁶u, hu=ab⁶t, iu=ab⁷t, ju=ab⁷s, ku=ab⁸s, lu=ab⁸r, mu=ab⁹r, nu=ab⁹q, ou=ab¹⁰q, pu=ab¹⁰p, qu=ab¹¹p, ru=ab¹¹o, su=ab¹²o, tu=b²⁵, u²=b²⁶, b⁶v=b⁵u, cv=ab²v, dv=ab³v, ev=ab⁴v, fv=ab⁵v, gv=ab⁵u, hv=ab⁶u, iv=ab⁶t, jv=ab⁷t, kv=ab⁷s, lv=ab⁸s, mv=ab⁸r, nv=ab⁹r, ov=ab⁹q, pv=ab¹⁰q, qv=ab¹⁰p, rv=ab¹¹p, sv=ab¹¹o, tv=ab¹²o, uv=b²⁵, v²=b²⁶, b⁵w=b⁴v, cw=ab²w, dw=ab³w, ew=ab⁴w, fw=ab⁴v, gw=ab⁵v, hw=ab⁵u, iw=ab⁶u, jw=ab⁶t, kw=ab⁷t, lw=ab⁷s, mw=ab⁸s, nw=ab⁸r, ow=ab⁹r, pw=ab⁹q, qw=ab¹⁰q, rw=ab¹⁰p, sw=ab¹¹p, tw=ab¹¹o, uw=ab¹²o, vw=b²⁵, w²=b²⁶, b⁴x=b³w, cx=ab²x, dx=ab³x, ex=ab³w, fx=ab⁴w, gx=ab⁴v, hx=ab⁵v, ix=ab⁵u, jx=ab⁶u, kx=ab⁶t, lx=ab⁷t, mx=ab⁷s, nx=ab⁸s, ox=ab⁸r, px=ab⁹r, qx=ab⁹q, rx=ab¹⁰q, sx=ab¹⁰p, tx=ab¹¹p, ux=ab¹¹o, vx=ab¹²o, wx=b²⁵, x²=b²⁶, b³y=b²x, cy=ab²y, dy=ab²x, ey=ab³x, fy=ab³w, gy=ab⁴w, hy=ab⁴v, iy=ab⁵v, jy=ab⁵u, ky=ab⁶u, ly=ab⁶t, my=ab⁷t, ny=ab⁷s, oy=ab⁸s, py=ab⁸r, qy=ab⁹r, ry=ab⁹q, sy=ab¹⁰q, ty=ab¹⁰p, uy=ab¹¹p, vy=ab¹¹o, wy=ab¹²o, xy=b²⁵, y²=b²⁶, b²z=by, cz=aby, dz=ab²y, ez=ab²x, fz=ab³x, gz=ab³w, hz=ab⁴w, iz=ab⁴v, jz=ab⁵v, kz=ab⁵u, lz=ab⁶u, mz=ab⁶t, nz=ab⁷t, oz=ab⁷s, pz=ab⁸s, qz=ab⁸r, rz=ab⁹r, sz=ab⁹q, tz=ab¹⁰q, uz=ab¹⁰p, vz=ab¹¹p, wz=ab¹¹o, xz=ab¹²o, yz=b²⁵, z²=b²⁶, bA=z, cA=abz, dA=aby, eA=ab²y, fA=ab²x, gA=ab³x, hA=ab³w, iA=ab⁴w, jA=ab⁴v, kA=ab⁵v, lA=ab⁵u, mA=ab⁶u, nA=ab⁶t, oA=ab⁷t, pA=ab⁷s, qA=ab⁸s, rA=ab⁸r, sA=ab⁹r, tA=ab⁹q, uA=ab¹⁰q, vA=ab¹⁰p, wA=ab¹¹p, xA=ab¹¹o, yA=ab¹²o, zA=b²⁵, A²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, ad, abe, af, ab²f, abg, ab³g, ah, ab²h, ab⁴h, abi, ab³i, ab⁵i, aj, ab²j, ab⁴j, ab⁶j, abk, ab³k, ab⁵k, ab⁷k, al, ab²l, ab⁴l, ab⁶l, ab⁸l, abm, ab³m, ab⁵m, ab⁷m, ab⁹m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, ab¹⁰n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, ab¹¹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, abs, ab³s, ab⁵s, ab⁷s, at, ab²t, ab⁴t, ab⁶t, abu, ab³u, ab⁵u, av, ab²v, ab⁴v, abw, ab³w, ax, ab²x, aby, az}

Phi = 1 a b a b ab b² ab b² c b³ ab² b³ d b⁴ ab³ b⁴ e b⁵ ab⁴ b⁵ f b⁶ ab⁵ b⁶ g b⁷ ab⁶ b⁷ h b⁸ ab⁷ b⁸ i b⁹ ab⁸ b⁹ j b¹⁰ ab⁹ b¹⁰ k b¹¹ ab¹⁰ b¹¹ l b¹² ab¹¹ b¹² m b¹³ ab¹² b¹³ n b¹⁴ ab¹³ b¹⁴ o b¹⁵ ab¹⁴ b¹⁵ p b¹⁶ ab¹⁵ b¹⁶ q b¹⁷ ab¹⁶ b¹⁷ r b¹⁸ ab¹⁷ b¹⁸ s b¹⁹ ab¹⁸ b¹⁹ t b²⁰ ab¹⁹ b²⁰ u b²¹ ab²⁰ b²¹ v b²² ab²¹ b²² w b²³ ab²² b²³ x b²⁴ ab²³ b²⁴ y b²⁵ ab²⁴ b²⁵ z b²⁶ ab²⁵ b²⁶ A b²⁵ ab²⁶ b²⁵

Monoid Structure