Details Page for 0.7123

Complete Solution is Known:

MSV File: q-0.7123.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₁₂(0.7123):

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, b²⁹=b²⁷, bc=b³, c²=b⁴, b²d=b⁵, cd=b⁵, d²=b⁶, b³e=b⁷, ce=b²e, de=b⁷, e²=b⁸, b⁴f=b⁹, cf=b²f, df=b³f, ef=b⁹, f²=b¹⁰, b⁵g=b¹¹, cg=b²g, dg=b³g, eg=b⁴g, fg=b¹¹, g²=b¹², b⁶h=b¹³, ch=b²h, dh=b³h, eh=b⁴h, fh=b⁵h, gh=b¹³, h²=b¹⁴, b⁷i=b¹⁵, ci=b²i, di=b³i, ei=b⁴i, fi=b⁵i, gi=b⁶i, hi=b¹⁵, i²=b¹⁶, b⁸j=b¹⁷, cj=b²j, dj=b³j, ej=b⁴j, fj=b⁵j, gj=b⁶j, hj=b⁷j, ij=b¹⁷, j²=b¹⁸, b⁹k=b¹⁹, ck=b²k, dk=b³k, ek=b⁴k, fk=b⁵k, gk=b⁶k, hk=b⁷k, ik=b⁸k, jk=b¹⁹, k²=b²⁰, b¹⁰l=b²¹, cl=b²l, dl=b³l, el=b⁴l, fl=b⁵l, gl=b⁶l, hl=b⁷l, il=b⁸l, jl=b⁹l, kl=b²¹, l²=b²², b¹¹m=b²³, cm=b²m, dm=b³m, em=b⁴m, fm=b⁵m, gm=b⁶m, hm=b⁷m, im=b⁸m, jm=b⁹m, km=b¹⁰m, lm=b²³, m²=b²⁴, b¹²n=b²⁵, cn=b²n, dn=b³n, en=b⁴n, fn=b⁵n, gn=b⁶n, hn=b⁷n, in=b⁸n, jn=b⁹n, kn=b¹⁰n, ln=b¹¹n, mn=b²⁵, n²=b²⁶, b¹³o=b²⁷, co=b²o, do=b³o, eo=b⁴o, fo=b⁵o, go=b⁶o, ho=b⁷o, io=b⁸o, jo=b⁹o, ko=b¹⁰o, lo=b¹¹o, mo=b¹²o, no=b²⁷, o²=b²⁸, b¹⁴p=b²⁷, cp=b²p, dp=b³p, ep=b⁴p, fp=b⁵p, gp=b⁶p, hp=b⁷p, ip=b⁸p, jp=b⁹p, kp=b¹⁰p, lp=b¹¹p, mp=b¹²p, np=b¹³p, op=b²⁷, p²=b²⁸, b¹³q=b¹²p, cq=b²q, dq=b³q, eq=b⁴q, fq=b⁵q, gq=b⁶q, hq=b⁷q, iq=b⁸q, jq=b⁹q, kq=b¹⁰q, lq=b¹¹q, mq=b¹²q, nq=b¹²p, oq=b¹³p, pq=b²⁷, q²=b²⁸, b¹²r=b¹¹q, cr=b²r, dr=b³r, er=b⁴r, fr=b⁵r, gr=b⁶r, hr=b⁷r, ir=b⁸r, jr=b⁹r, kr=b¹⁰r, lr=b¹¹r, mr=b¹¹q, nr=b¹²q, or=b¹²p, pr=b¹³p, qr=b²⁷, r²=b²⁸, b¹¹s=b¹⁰r, cs=b²s, ds=b³s, es=b⁴s, fs=b⁵s, gs=b⁶s, hs=b⁷s, is=b⁸s, js=b⁹s, ks=b¹⁰s, ls=b¹⁰r, ms=b¹¹r, ns=b¹¹q, os=b¹²q, ps=b¹²p, qs=b¹³p, rs=b²⁷, s²=b²⁸, b¹⁰t=b⁹s, ct=b²t, dt=b³t, et=b⁴t, ft=b⁵t, gt=b⁶t, ht=b⁷t, it=b⁸t, jt=b⁹t, kt=b⁹s, lt=b¹⁰s, mt=b¹⁰r, nt=b¹¹r, ot=b¹¹q, pt=b¹²q, qt=b¹²p, rt=b¹³p, st=b²⁷, t²=b²⁸, b⁹u=b⁸t, cu=b²u, du=b³u, eu=b⁴u, fu=b⁵u, gu=b⁶u, hu=b⁷u, iu=b⁸u, ju=b⁸t, ku=b⁹t, lu=b⁹s, mu=b¹⁰s, nu=b¹⁰r, ou=b¹¹r, pu=b¹¹q, qu=b¹²q, ru=b¹²p, su=b¹³p, tu=b²⁷, u²=b²⁸, b⁸v=b⁷u, cv=b²v, dv=b³v, ev=b⁴v, fv=b⁵v, gv=b⁶v, hv=b⁷v, iv=b⁷u, jv=b⁸u, kv=b⁸t, lv=b⁹t, mv=b⁹s, nv=b¹⁰s, ov=b¹⁰r, pv=b¹¹r, qv=b¹¹q, rv=b¹²q, sv=b¹²p, tv=b¹³p, uv=b²⁷, v²=b²⁸, b⁷w=b⁶v, cw=b²w, dw=b³w, ew=b⁴w, fw=b⁵w, gw=b⁶w, hw=b⁶v, iw=b⁷v, jw=b⁷u, kw=b⁸u, lw=b⁸t, mw=b⁹t, nw=b⁹s, ow=b¹⁰s, pw=b¹⁰r, qw=b¹¹r, rw=b¹¹q, sw=b¹²q, tw=b¹²p, uw=b¹³p, vw=b²⁷, w²=b²⁸, b⁶x=b⁵w, cx=b²x, dx=b³x, ex=b⁴x, fx=b⁵x, gx=b⁵w, hx=b⁶w, ix=b⁶v, jx=b⁷v, kx=b⁷u, lx=b⁸u, mx=b⁸t, nx=b⁹t, ox=b⁹s, px=b¹⁰s, qx=b¹⁰r, rx=b¹¹r, sx=b¹¹q, tx=b¹²q, ux=b¹²p, vx=b¹³p, wx=b²⁷, x²=b²⁸, b⁵y=b⁴x, cy=b²y, dy=b³y, ey=b⁴y, fy=b⁴x, gy=b⁵x, hy=b⁵w, iy=b⁶w, jy=b⁶v, ky=b⁷v, ly=b⁷u, my=b⁸u, ny=b⁸t, oy=b⁹t, py=b⁹s, qy=b¹⁰s, ry=b¹⁰r, sy=b¹¹r, ty=b¹¹q, uy=b¹²q, vy=b¹²p, wy=b¹³p, xy=b²⁷, y²=b²⁸, b⁴z=b³y, cz=b²z, dz=b³z, ez=b³y, fz=b⁴y, gz=b⁴x, hz=b⁵x, iz=b⁵w, jz=b⁶w, kz=b⁶v, lz=b⁷v, mz=b⁷u, nz=b⁸u, oz=b⁸t, pz=b⁹t, qz=b⁹s, rz=b¹⁰s, sz=b¹⁰r, tz=b¹¹r, uz=b¹¹q, vz=b¹²q, wz=b¹²p, xz=b¹³p, yz=b²⁷, z²=b²⁸, b³A=b²z, cA=b²A, dA=b²z, eA=b³z, fA=b³y, gA=b⁴y, hA=b⁴x, iA=b⁵x, jA=b⁵w, kA=b⁶w, lA=b⁶v, mA=b⁷v, nA=b⁷u, oA=b⁸u, pA=b⁸t, qA=b⁹t, rA=b⁹s, sA=b¹⁰s, tA=b¹⁰r, uA=b¹¹r, vA=b¹¹q, wA=b¹²q, xA=b¹²p, yA=b¹³p, zA=b²⁷, A²=b²⁸, b³B=bA, cB=b²B, dB=bA, eB=b²A, fB=b²z, gB=b³z, hB=b³y, iB=b⁴y, jB=b⁴x, kB=b⁵x, lB=b⁵w, mB=b⁶w, nB=b⁶v, oB=b⁷v, pB=b⁷u, qB=b⁸u, rB=b⁸t, sB=b⁹t, tB=b⁹s, uB=b¹⁰s, vB=b¹⁰r, wB=b¹¹r, xB=b¹¹q, yB=b¹²q, zB=b¹²p, AB=b¹³p, B²=b²⁸>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, b²⁸, d, be, f, b²f, bg, b³g, h, b²h, b⁴h, bi, b³i, b⁵i, j, b²j, b⁴j, b⁶j, bk, b³k, b⁵k, b⁷k, l, b²l, b⁴l, b⁶l, b⁸l, bm, b³m, b⁵m, b⁷m, b⁹m, n, b²n, b⁴n, b⁶n, b⁸n, b¹⁰n, bo, b³o, b⁵o, b⁷o, b⁹o, b¹¹o, p, b²p, b⁴p, b⁶p, b⁸p, b¹⁰p, b¹²p, bq, b³q, b⁵q, b⁷q, b⁹q, b¹¹q, r, b²r, b⁴r, b⁶r, b⁸r, b¹⁰r, bs, b³s, b⁵s, b⁷s, b⁹s, t, b²t, b⁴t, b⁶t, b⁸t, bu, b³u, b⁵u, b⁷u, v, b²v, b⁴v, b⁶v, bw, b³w, b⁵w, x, b²x, b⁴x, by, b³y, z, b²z, bA, bB}

Phi = 1 a b a b ab 1 ab c ac b ab² d ab³ b² ab³ e ab⁴ b³ ab⁴ f ab⁵ b⁴ ab⁵ g ab⁶ b⁵ ab⁶ h ab⁷ b⁶ ab⁷ i ab⁸ b⁷ ab⁸ j ab⁹ b⁸ ab⁹ k ab¹⁰ b⁹ ab¹⁰ l ab¹¹ b¹⁰ ab¹¹ m ab¹² b¹¹ ab¹² n ab¹³ b¹² ab¹³ o ab¹⁴ b¹³ ab¹⁴ p ab¹⁵ b¹⁴ ab¹⁵ q ab¹⁶ b¹⁵ ab¹⁶ r ab¹⁷ b¹⁶ ab¹⁷ s ab¹⁸ b¹⁷ ab¹⁸ t ab¹⁹ b¹⁸ ab¹⁹ u ab²⁰ b¹⁹ ab²⁰ v ab²¹ b²⁰ ab²¹ w ab²² b²¹ ab²² x ab²³ b²² ab²³ y ab²⁴ b²³ ab²⁴ z ab²⁵ b²⁴ ab²⁵ A ab²⁶ b²⁵ ab²⁶ bB ab²⁷ b²⁶ ab²⁷ B ab²⁸ b²⁷ ab²⁸

Monoid Structure