Details Page for 0.7541

Complete Solution is Known:

MSV File: q-0.7541.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₃₁(0.7541):

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, b²⁵=b²³, bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, be=ab⁷, ce=b⁸, de=b¹⁰, e²=b¹², b²f=b⁹, cf=ab⁹, df=ab¹¹, ef=ab¹³, f²=b¹⁴, b³g=ab¹¹, cg=ab²g, dg=b¹², eg=b¹⁴, fg=ab¹⁵, g²=b¹⁶, b⁴h=b¹³, ch=ab²h, dh=ab¹³, eh=ab¹⁵, fh=b¹⁶, gh=ab¹⁷, h²=b¹⁸, b⁵i=ab¹⁵, ci=ab²i, di=ab⁴i, ei=b¹⁶, fi=ab¹⁷, gi=b¹⁸, hi=ab¹⁹, i²=b²⁰, b⁶j=b¹⁷, cj=ab²j, dj=ab⁴j, ej=ab¹⁷, fj=b¹⁸, gj=ab¹⁹, hj=b²⁰, ij=ab²¹, j²=b²², b⁷k=ab¹⁹, ck=ab²k, dk=ab⁴k, ek=ab⁶k, fk=ab¹⁹, gk=b²⁰, hk=ab²¹, ik=b²², jk=ab²³, k²=b²⁴, b⁸l=b²¹, cl=ab²l, dl=ab⁴l, el=ab⁶l, fl=b⁷l, gl=ab²¹, hl=b²², il=ab²³, jl=b²⁴, kl=ab²³, l²=b²⁴, b⁹m=ab²³, cm=ab²m, dm=ab⁴m, em=ab⁶m, fm=b⁷m, gm=ab⁸m, hm=ab²³, im=b²⁴, jm=ab²³, km=b²⁴, lm=ab²³, m²=b²⁴, b¹⁰n=b²³, cn=ab²n, dn=ab⁴n, en=ab⁶n, fn=b⁷n, gn=ab⁸n, hn=b⁹n, in=ab²³, jn=b²⁴, kn=ab²³, ln=b²⁴, mn=ab²³, n²=b²⁴, b⁹o=ab⁸n, co=ab²o, do=ab⁴o, eo=ab⁶o, fo=b⁷o, go=ab⁸o, ho=ab⁸n, io=b⁹n, jo=ab²³, ko=b²⁴, lo=ab²³, mo=b²⁴, no=ab²³, o²=b²⁴, b⁸p=ab⁷o, cp=ab²p, dp=ab⁴p, ep=ab⁶p, fp=b⁷p, gp=b⁷o, hp=ab⁸o, ip=ab⁸n, jp=b⁹n, kp=ab²³, lp=b²⁴, mp=ab²³, np=b²⁴, op=ab²³, p²=b²⁴, b⁷q=ab⁶p, cq=ab²q, dq=ab⁴q, eq=ab⁶q, fq=ab⁶p, gq=b⁷p, hq=b⁷o, iq=ab⁸o, jq=ab⁸n, kq=b⁹n, lq=ab²³, mq=b²⁴, nq=ab²³, oq=b²⁴, pq=ab²³, q²=b²⁴, b⁶r=ab⁵q, cr=ab²r, dr=ab⁴r, er=b⁵q, fr=ab⁶q, gr=ab⁶p, hr=b⁷p, ir=b⁷o, jr=ab⁸o, kr=ab⁸n, lr=b⁹n, mr=ab²³, nr=b²⁴, or=ab²³, pr=b²⁴, qr=ab²³, r²=b²⁴, b⁵s=ab⁴r, cs=ab²s, ds=ab⁴s, es=b⁵r, fs=b⁵q, gs=ab⁶q, hs=ab⁶p, is=b⁷p, js=b⁷o, ks=ab⁸o, ls=ab⁸n, ms=b⁹n, ns=ab²³, os=b²⁴, ps=ab²³, qs=b²⁴, rs=ab²³, s²=b²⁴, b⁴t=ab³s, ct=ab²t, dt=b³s, et=ab⁴r, ft=b⁵r, gt=b⁵q, ht=ab⁶q, it=ab⁶p, jt=b⁷p, kt=b⁷o, lt=ab⁸o, mt=ab⁸n, nt=b⁹n, ot=ab²³, pt=b²⁴, qt=ab²³, rt=b²⁴, st=ab²³, t²=b²⁴, b³u=ab²t, cu=ab²u, du=b³t, eu=ab⁴s, fu=ab⁴r, gu=b⁵r, hu=b⁵q, iu=ab⁶q, ju=ab⁶p, ku=b⁷p, lu=b⁷o, mu=ab⁸o, nu=ab⁸n, ou=b⁹n, pu=ab²³, qu=b²⁴, ru=ab²³, su=b²⁴, tu=ab²³, u²=b²⁴, b²v=abu, cv=bu, dv=ab²t, ev=b³s, fv=ab⁴s, gv=ab⁴r, hv=b⁵r, iv=b⁵q, jv=ab⁶q, kv=ab⁶p, lv=b⁷p, mv=b⁷o, nv=ab⁸o, ov=ab⁸n, pv=b⁹n, qv=ab²³, rv=b²⁴, sv=ab²³, tv=b²⁴, uv=ab²³, v²=b²⁴, bw=av, cw=bv, dw=ab²u, ew=b³t, fw=b³s, gw=ab⁴s, hw=ab⁴r, iw=b⁵r, jw=b⁵q, kw=ab⁶q, lw=ab⁶p, mw=b⁷p, nw=b⁷o, ow=ab⁸o, pw=ab⁸n, qw=b⁹n, rw=ab²³, sw=b²⁴, tw=ab²³, uw=b²⁴, vw=ab²³, w²=b²⁴, bx=aw, cx=av, dx=bu, ex=ab²t, fx=b³t, gx=b³s, hx=ab⁴s, ix=ab⁴r, jx=b⁵r, kx=b⁵q, lx=ab⁶q, mx=ab⁶p, nx=b⁷p, ox=b⁷o, px=ab⁸o, qx=ab⁸n, rx=b⁹n, sx=ab²³, tx=b²⁴, ux=ab²³, vx=b²⁴, wx=ab²³, x²=b²⁴, by=ax, cy=aw, dy=bv, ey=ab²u, fy=ab²t, gy=b³t, hy=b³s, iy=ab⁴s, jy=ab⁴r, ky=b⁵r, ly=b⁵q, my=ab⁶q, ny=ab⁶p, oy=b⁷p, py=b⁷o, qy=ab⁸o, ry=ab⁸n, sy=b⁹n, ty=ab²³, uy=b²⁴, vy=ab²³, wy=b²⁴, xy=ab²³, y²=b²⁴, bz=ay, cz=ax, dz=av, ez=bu, fz=ab²u, gz=ab²t, hz=b³t, iz=b³s, jz=ab⁴s, kz=ab⁴r, lz=b⁵r, mz=b⁵q, nz=ab⁶q, oz=ab⁶p, pz=b⁷p, qz=b⁷o, rz=ab⁸o, sz=ab⁸n, tz=b⁹n, uz=ab²³, vz=b²⁴, wz=ab²³, xz=b²⁴, yz=ab²³, z²=b²⁴, bA=az, cA=ay, dA=aw, eA=bv, fA=bu, gA=ab²u, hA=ab²t, iA=b³t, jA=b³s, kA=ab⁴s, lA=ab⁴r, mA=b⁵r, nA=b⁵q, oA=ab⁶q, pA=ab⁶p, qA=b⁷p, rA=b⁷o, sA=ab⁸o, tA=ab⁸n, uA=b⁹n, vA=ab²³, wA=b²⁴, xA=ab²³, yA=b²⁴, zA=ab²³, A²=b²⁴>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, af, bg, ah, ab²h, bi, b³i, aj, ab²j, ab⁴j, bk, b³k, b⁵k, al, ab²l, ab⁴l, ab⁶l, bm, b³m, b⁵m, b⁷m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, bo, b³o, b⁵o, b⁷o, ap, ab²p, ab⁴p, ab⁶p, bq, b³q, b⁵q, ar, ab²r, ab⁴r, bs, b³s, at, ab²t, bu, av, ax, az}

Phi = 1 a b a b c b³ d b⁵ e f g h i j k l m n o p q r s t u v w x y z A

Monoid Structure