Details Page for 0.3271

Complete Solution is Known:

MSV File: q-0.3271.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₆₀(0.3271):

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 | a²=1, b²⁸=b²⁶, bc=ab³, c²=b⁴, b²d=ab⁵, cd=b⁵, d²=b⁶, b³e=b⁷, ce=ab²e, de=ab⁷, e²=b⁸, b⁴f=ab⁹, cf=ab²f, df=ab³f, ef=ab⁹, f²=b¹⁰, b⁵g=b¹¹, cg=ab²g, dg=ab³g, eg=b⁴g, fg=ab¹¹, g²=b¹², b⁶h=ab¹³, ch=ab²h, dh=ab³h, eh=b⁴h, fh=ab⁵h, gh=ab¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=ab²i, di=ab³i, ei=b⁴i, fi=ab⁵i, gi=b⁶i, hi=ab¹⁵, i²=b¹⁶, b⁸j=ab¹⁷, cj=ab²j, dj=ab³j, ej=b⁴j, fj=ab⁵j, gj=b⁶j, hj=ab⁷j, ij=ab¹⁷, j²=b¹⁸, b⁹k=b¹⁹, ck=ab²k, dk=ab³k, ek=b⁴k, fk=ab⁵k, gk=b⁶k, hk=ab⁷k, ik=b⁸k, jk=ab¹⁹, k²=b²⁰, b¹⁰l=ab²¹, cl=ab²l, dl=ab³l, el=b⁴l, fl=ab⁵l, gl=b⁶l, hl=ab⁷l, il=b⁸l, jl=ab⁹l, kl=ab²¹, l²=b²², b¹¹m=b²³, cm=ab²m, dm=ab³m, em=b⁴m, fm=ab⁵m, gm=b⁶m, hm=ab⁷m, im=b⁸m, jm=ab⁹m, km=b¹⁰m, lm=ab²³, m²=b²⁴, b¹²n=ab²⁵, cn=ab²n, dn=ab³n, en=b⁴n, fn=ab⁵n, gn=b⁶n, hn=ab⁷n, in=b⁸n, jn=ab⁹n, kn=b¹⁰n, ln=ab¹¹n, mn=ab²⁵, n²=b²⁶, b¹³o=b²⁷, co=ab²o, do=ab³o, eo=b⁴o, fo=ab⁵o, go=b⁶o, ho=ab⁷o, io=b⁸o, jo=ab⁹o, ko=b¹⁰o, lo=ab¹¹o, mo=b¹²o, no=ab²⁷, o²=b²⁶, b¹³p=ab¹²o, cp=ab²p, dp=ab³p, ep=b⁴p, fp=ab⁵p, gp=b⁶p, hp=ab⁷p, ip=b⁸p, jp=ab⁹p, kp=b¹⁰p, lp=ab¹¹p, mp=b¹²p, np=b¹²o, op=ab²⁷, p²=b²⁶, b¹²q=ab¹¹p, cq=ab²q, dq=ab³q, eq=b⁴q, fq=ab⁵q, gq=b⁶q, hq=ab⁷q, iq=b⁸q, jq=ab⁹q, kq=b¹⁰q, lq=ab¹¹q, mq=ab¹¹p, nq=b¹²p, oq=b¹²o, pq=ab²⁷, q²=b²⁶, b¹¹r=ab¹⁰q, cr=ab²r, dr=ab³r, er=b⁴r, fr=ab⁵r, gr=b⁶r, hr=ab⁷r, ir=b⁸r, jr=ab⁹r, kr=b¹⁰r, lr=b¹⁰q, mr=ab¹¹q, nr=ab¹¹p, or=b¹²p, pr=b¹²o, qr=ab²⁷, r²=b²⁶, b¹⁰s=ab⁹r, cs=ab²s, ds=ab³s, es=b⁴s, fs=ab⁵s, gs=b⁶s, hs=ab⁷s, is=b⁸s, js=ab⁹s, ks=ab⁹r, ls=b¹⁰r, ms=b¹⁰q, ns=ab¹¹q, os=ab¹¹p, ps=b¹²p, qs=b¹²o, rs=ab²⁷, s²=b²⁶, b⁹t=ab⁸s, ct=ab²t, dt=ab³t, et=b⁴t, ft=ab⁵t, gt=b⁶t, ht=ab⁷t, it=b⁸t, jt=b⁸s, kt=ab⁹s, lt=ab⁹r, mt=b¹⁰r, nt=b¹⁰q, ot=ab¹¹q, pt=ab¹¹p, qt=b¹²p, rt=b¹²o, st=ab²⁷, t²=b²⁶, b⁸u=ab⁷t, cu=ab²u, du=ab³u, eu=b⁴u, fu=ab⁵u, gu=b⁶u, hu=ab⁷u, iu=ab⁷t, ju=b⁸t, ku=b⁸s, lu=ab⁹s, mu=ab⁹r, nu=b¹⁰r, ou=b¹⁰q, pu=ab¹¹q, qu=ab¹¹p, ru=b¹²p, su=b¹²o, tu=ab²⁷, u²=b²⁶, b⁷v=ab⁶u, cv=ab²v, dv=ab³v, ev=b⁴v, fv=ab⁵v, gv=b⁶v, hv=b⁶u, iv=ab⁷u, jv=ab⁷t, kv=b⁸t, lv=b⁸s, mv=ab⁹s, nv=ab⁹r, ov=b¹⁰r, pv=b¹⁰q, qv=ab¹¹q, rv=ab¹¹p, sv=b¹²p, tv=b¹²o, uv=ab²⁷, v²=b²⁶, b⁶w=ab⁵v, cw=ab²w, dw=ab³w, ew=b⁴w, fw=ab⁵w, gw=ab⁵v, hw=b⁶v, iw=b⁶u, jw=ab⁷u, kw=ab⁷t, lw=b⁸t, mw=b⁸s, nw=ab⁹s, ow=ab⁹r, pw=b¹⁰r, qw=b¹⁰q, rw=ab¹¹q, sw=ab¹¹p, tw=b¹²p, uw=b¹²o, vw=ab²⁷, w²=b²⁶, b⁵x=ab⁴w, cx=ab²x, dx=ab³x, ex=b⁴x, fx=b⁴w, gx=ab⁵w, hx=ab⁵v, ix=b⁶v, jx=b⁶u, kx=ab⁷u, lx=ab⁷t, mx=b⁸t, nx=b⁸s, ox=ab⁹s, px=ab⁹r, qx=b¹⁰r, rx=b¹⁰q, sx=ab¹¹q, tx=ab¹¹p, ux=b¹²p, vx=b¹²o, wx=ab²⁷, x²=b²⁶, b⁴y=ab³x, cy=ab²y, dy=ab³y, ey=ab³x, fy=b⁴x, gy=b⁴w, hy=ab⁵w, iy=ab⁵v, jy=b⁶v, ky=b⁶u, ly=ab⁷u, my=ab⁷t, ny=b⁸t, oy=b⁸s, py=ab⁹s, qy=ab⁹r, ry=b¹⁰r, sy=b¹⁰q, ty=ab¹¹q, uy=ab¹¹p, vy=b¹²p, wy=b¹²o, xy=ab²⁷, y²=b²⁶, b³z=ab²y, cz=ab²z, dz=b²y, ez=ab³y, fz=ab³x, gz=b⁴x, hz=b⁴w, iz=ab⁵w, jz=ab⁵v, kz=b⁶v, lz=b⁶u, mz=ab⁷u, nz=ab⁷t, oz=b⁸t, pz=b⁸s, qz=ab⁹s, rz=ab⁹r, sz=b¹⁰r, tz=b¹⁰q, uz=ab¹¹q, vz=ab¹¹p, wz=b¹²p, xz=b¹²o, yz=ab²⁷, z²=b²⁶, b²A=abz, cA=bz, dA=b²z, eA=b²y, fA=ab³y, gA=ab³x, hA=b⁴x, iA=b⁴w, jA=ab⁵w, kA=ab⁵v, lA=b⁶v, mA=b⁶u, nA=ab⁷u, oA=ab⁷t, pA=b⁸t, qA=b⁸s, rA=ab⁹s, sA=ab⁹r, tA=b¹⁰r, uA=b¹⁰q, vA=ab¹¹q, wA=ab¹¹p, xA=b¹²p, yA=b¹²o, zA=ab²⁷, A²=b²⁶, bB=aA, cB=bA, dB=abz, eB=b²z, fB=b²y, gB=ab³y, hB=ab³x, iB=b⁴x, jB=b⁴w, kB=ab⁵w, lB=ab⁵v, mB=b⁶v, nB=b⁶u, oB=ab⁷u, pB=ab⁷t, qB=b⁸t, rB=b⁸s, sB=ab⁹s, tB=ab⁹r, uB=b¹⁰r, vB=b¹⁰q, wB=ab¹¹q, xB=ab¹¹p, yB=b¹²p, zB=b¹²o, AB=ab²⁷, B²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, d, abe, f, b²f, abg, ab³g, h, b²h, b⁴h, abi, ab³i, ab⁵i, j, b²j, b⁴j, b⁶j, abk, ab³k, ab⁵k, ab⁷k, l, b²l, b⁴l, b⁶l, b⁸l, abm, ab³m, ab⁵m, ab⁷m, ab⁹m, n, b²n, b⁴n, b⁶n, b⁸n, b¹⁰n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, ab¹¹o, p, b²p, b⁴p, b⁶p, b⁸p, b¹⁰p, b¹²p, abq, ab³q, ab⁵q, ab⁷q, ab⁹q, ab¹¹q, r, b²r, b⁴r, b⁶r, b⁸r, b¹⁰r, abs, ab³s, ab⁵s, ab⁷s, ab⁹s, t, b²t, b⁴t, b⁶t, b⁸t, abu, ab³u, ab⁵u, ab⁷u, v, b²v, b⁴v, b⁶v, abw, ab³w, ab⁵w, x, b²x, b⁴x, aby, ab³y, z, b²z, abA, B}

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

Monoid Structure