Details Page for 0.2224

Complete Solution is Known:

MSV File: q-0.2224.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₇₂(0.2224):

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 | a²=1, b³⁰=b²⁸, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², b²f=ab⁹, cf=b⁹, df=b¹¹, ef=b¹³, f²=b¹⁴, b³g=ab¹¹, cg=ab²g, dg=b¹², eg=b¹⁴, fg=b¹⁵, g²=b¹⁶, b⁴h=ab¹³, ch=ab²h, dh=b¹³, eh=b¹⁵, fh=b¹⁶, gh=b¹⁷, h²=b¹⁸, b⁵i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=b¹⁶, fi=b¹⁷, gi=b¹⁸, hi=b¹⁹, i²=b²⁰, b⁶j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b¹⁷, fj=b¹⁸, gj=b¹⁹, hj=b²⁰, ij=b²¹, j²=b²², b⁷k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁶k, fk=b¹⁹, gk=b²⁰, hk=b²¹, ik=b²², jk=b²³, k²=b²⁴, b⁸l=ab²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=ab⁷l, gl=b²¹, hl=b²², il=b²³, jl=b²⁴, kl=b²⁵, l²=b²⁶, b⁹m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=ab⁷m, gm=ab⁸m, hm=b²³, im=b²⁴, jm=b²⁵, km=b²⁶, lm=b²⁷, m²=b²⁸, b¹⁰n=ab²⁵, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=ab⁷n, gn=ab⁸n, hn=ab⁹n, in=b²⁵, jn=b²⁶, kn=b²⁷, ln=b²⁸, mn=b²⁹, n²=b²⁸, b¹¹o=ab²⁷, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=ab⁷o, go=ab⁸o, ho=ab⁹o, io=ab¹⁰o, jo=b²⁷, ko=b²⁸, lo=b²⁹, mo=b²⁸, no=b²⁹, o²=b²⁸, b¹²p=ab²⁹, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=ab⁷p, gp=ab⁸p, hp=ab⁹p, ip=ab¹⁰p, jp=ab¹¹p, kp=b²⁹, lp=b²⁸, mp=b²⁹, np=b²⁸, op=b²⁹, p²=b²⁸, b¹²q=b¹¹p, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁷q, gq=ab⁸q, hq=ab⁹q, iq=ab¹⁰q, jq=ab¹¹q, kq=ab¹¹p, lq=b²⁹, mq=b²⁸, nq=b²⁹, oq=b²⁸, pq=b²⁹, q²=b²⁸, b¹¹r=b¹⁰q, cr=ab²r, dr=ab⁴r, er=ab⁶r, fr=ab⁷r, gr=ab⁸r, hr=ab⁹r, ir=ab¹⁰r, jr=ab¹⁰q, kr=ab¹¹q, lr=ab¹¹p, mr=b²⁹, nr=b²⁸, or=b²⁹, pr=b²⁸, qr=b²⁹, r²=b²⁸, b¹⁰s=b⁹r, cs=ab²s, ds=ab⁴s, es=ab⁶s, fs=ab⁷s, gs=ab⁸s, hs=ab⁹s, is=ab⁹r, js=ab¹⁰r, ks=ab¹⁰q, ls=ab¹¹q, ms=ab¹¹p, ns=b²⁹, os=b²⁸, ps=b²⁹, qs=b²⁸, rs=b²⁹, s²=b²⁸, b⁹t=b⁸s, ct=ab²t, dt=ab⁴t, et=ab⁶t, ft=ab⁷t, gt=ab⁸t, ht=ab⁸s, it=ab⁹s, jt=ab⁹r, kt=ab¹⁰r, lt=ab¹⁰q, mt=ab¹¹q, nt=ab¹¹p, ot=b²⁹, pt=b²⁸, qt=b²⁹, rt=b²⁸, st=b²⁹, t²=b²⁸, b⁸u=b⁷t, cu=ab²u, du=ab⁴u, eu=ab⁶u, fu=ab⁷u, gu=ab⁷t, hu=ab⁸t, iu=ab⁸s, ju=ab⁹s, ku=ab⁹r, lu=ab¹⁰r, mu=ab¹⁰q, nu=ab¹¹q, ou=ab¹¹p, pu=b²⁹, qu=b²⁸, ru=b²⁹, su=b²⁸, tu=b²⁹, u²=b²⁸, b⁷v=b⁶u, cv=ab²v, dv=ab⁴v, ev=ab⁶v, fv=ab⁶u, gv=ab⁷u, hv=ab⁷t, iv=ab⁸t, jv=ab⁸s, kv=ab⁹s, lv=ab⁹r, mv=ab¹⁰r, nv=ab¹⁰q, ov=ab¹¹q, pv=ab¹¹p, qv=b²⁹, rv=b²⁸, sv=b²⁹, tv=b²⁸, uv=b²⁹, v²=b²⁸, b⁶w=b⁵v, cw=ab²w, dw=ab⁴w, ew=ab⁵v, fw=ab⁶v, gw=ab⁶u, hw=ab⁷u, iw=ab⁷t, jw=ab⁸t, kw=ab⁸s, lw=ab⁹s, mw=ab⁹r, nw=ab¹⁰r, ow=ab¹⁰q, pw=ab¹¹q, qw=ab¹¹p, rw=b²⁹, sw=b²⁸, tw=b²⁹, uw=b²⁸, vw=b²⁹, w²=b²⁸, b⁵x=b⁴w, cx=ab²x, dx=ab⁴x, ex=ab⁵w, fx=ab⁵v, gx=ab⁶v, hx=ab⁶u, ix=ab⁷u, jx=ab⁷t, kx=ab⁸t, lx=ab⁸s, mx=ab⁹s, nx=ab⁹r, ox=ab¹⁰r, px=ab¹⁰q, qx=ab¹¹q, rx=ab¹¹p, sx=b²⁹, tx=b²⁸, ux=b²⁹, vx=b²⁸, wx=b²⁹, x²=b²⁸, b⁴y=b³x, cy=ab²y, dy=ab³x, ey=ab⁴w, fy=ab⁵w, gy=ab⁵v, hy=ab⁶v, iy=ab⁶u, jy=ab⁷u, ky=ab⁷t, ly=ab⁸t, my=ab⁸s, ny=ab⁹s, oy=ab⁹r, py=ab¹⁰r, qy=ab¹⁰q, ry=ab¹¹q, sy=ab¹¹p, ty=b²⁹, uy=b²⁸, vy=b²⁹, wy=b²⁸, xy=b²⁹, y²=b²⁸, b³z=b²y, cz=ab²z, dz=ab³y, ez=ab⁴x, fz=ab⁴w, gz=ab⁵w, hz=ab⁵v, iz=ab⁶v, jz=ab⁶u, kz=ab⁷u, lz=ab⁷t, mz=ab⁸t, nz=ab⁸s, oz=ab⁹s, pz=ab⁹r, qz=ab¹⁰r, rz=ab¹⁰q, sz=ab¹¹q, tz=ab¹¹p, uz=b²⁹, vz=b²⁸, wz=b²⁹, xz=b²⁸, yz=b²⁹, z²=b²⁸, b²A=bz, cA=abz, dA=ab²y, eA=ab³x, fA=ab⁴x, gA=ab⁴w, hA=ab⁵w, iA=ab⁵v, jA=ab⁶v, kA=ab⁶u, lA=ab⁷u, mA=ab⁷t, nA=ab⁸t, oA=ab⁸s, pA=ab⁹s, qA=ab⁹r, rA=ab¹⁰r, sA=ab¹⁰q, tA=ab¹¹q, uA=ab¹¹p, vA=b²⁹, wA=b²⁸, xA=b²⁹, yA=b²⁸, zA=b²⁹, A²=b²⁸, bB=A, cB=abA, dB=ab²z, eB=ab³y, fB=ab³x, gB=ab⁴x, hB=ab⁴w, iB=ab⁵w, jB=ab⁵v, kB=ab⁶v, lB=ab⁶u, mB=ab⁷u, nB=ab⁷t, oB=ab⁸t, pB=ab⁸s, qB=ab⁹s, rB=ab⁹r, sB=ab¹⁰r, tB=ab¹⁰q, uB=ab¹¹q, vB=ab¹¹p, wB=b²⁹, xB=b²⁸, yB=b²⁹, zB=b²⁸, AB=b²⁹, B²=b²⁸, b⁴C=B, cC=ab²C, dC=aB, eC=abA, fC=abz, gC=ab²z, hC=ab²y, iC=ab³y, jC=ab³x, kC=ab⁴x, lC=ab⁴w, mC=ab⁵w, nC=ab⁵v, oC=ab⁶v, pC=ab⁶u, qC=ab⁷u, rC=ab⁷t, sC=ab⁸t, tC=ab⁸s, uC=ab⁹s, vC=ab⁹r, wC=ab¹⁰r, xC=ab¹⁰q, yC=ab¹¹q, zC=ab¹¹p, AC=b²⁹, BC=b²⁸, C²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, af, abg, ah, ab²h, abi, ab³i, aj, ab²j, ab⁴j, abk, ab³k, ab⁵k, al, ab²l, ab⁴l, ab⁶l, abm, ab³m, ab⁵m, ab⁷m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, ab¹¹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, ab¹⁰r, abs, ab³s, ab⁵s, ab⁷s, ab⁹s, at, ab²t, ab⁴t, ab⁶t, ab⁸t, abu, ab³u, ab⁵u, ab⁷u, av, ab²v, ab⁴v, ab⁶v, abw, ab³w, ab⁵w, ax, ab²x, ab⁴x, aby, ab³y, az, ab²z, abA, aB, aC, ab²C}

Phi = 1 1 a b ab 1 a b ab 1 c b ab³ b² d b³ ab⁵ b⁴ e b⁵ f b⁶ g b⁷ h b⁸ i b⁹ j b¹⁰ k b¹¹ l b¹² m b¹³ n b¹⁴ o b¹⁵ p b¹⁶ q b¹⁷ r b¹⁸ s b¹⁹ t b²⁰ u b²¹ v b²² w b²³ x b²⁴ y b²⁵ z b²⁶ A b²⁷ B b²⁸ b³C b²⁹ b²C b²⁸ bC b²⁹ C b²⁸

Monoid Structure