Details Page for 0.7561

Complete Solution is Known:

MSV File: q-0.7561.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₂(0.7561):

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, b²⁸=b²⁶, bc=ab³, c²=b⁴, b²d=b⁵, cd=ab⁵, d²=b⁶, b³e=ab⁷, ce=ab²e, de=ab⁷, e²=b⁸, b⁴f=b⁹, cf=ab²f, df=b³f, ef=ab⁹, f²=b¹⁰, b⁵g=ab¹¹, cg=ab²g, dg=b³g, eg=ab⁴g, fg=ab¹¹, g²=b¹², b⁶h=b¹³, ch=ab²h, dh=b³h, eh=ab⁴h, fh=b⁵h, gh=ab¹³, h²=b¹⁴, b⁷i=ab¹⁵, ci=ab²i, di=b³i, ei=ab⁴i, fi=b⁵i, gi=ab⁶i, hi=ab¹⁵, i²=b¹⁶, b⁸j=b¹⁷, cj=ab²j, dj=b³j, ej=ab⁴j, fj=b⁵j, gj=ab⁶j, hj=b⁷j, ij=ab¹⁷, j²=b¹⁸, b⁹k=ab¹⁹, ck=ab²k, dk=b³k, ek=ab⁴k, fk=b⁵k, gk=ab⁶k, hk=b⁷k, ik=ab⁸k, jk=ab¹⁹, k²=b²⁰, b¹⁰l=b²¹, cl=ab²l, dl=b³l, el=ab⁴l, fl=b⁵l, gl=ab⁶l, hl=b⁷l, il=ab⁸l, jl=b⁹l, kl=ab²¹, l²=b²², b¹¹m=ab²³, cm=ab²m, dm=b³m, em=ab⁴m, fm=b⁵m, gm=ab⁶m, hm=b⁷m, im=ab⁸m, jm=b⁹m, km=ab¹⁰m, lm=ab²³, m²=b²⁴, b¹²n=b²⁵, cn=ab²n, dn=b³n, en=ab⁴n, fn=b⁵n, gn=ab⁶n, hn=b⁷n, in=ab⁸n, jn=b⁹n, kn=ab¹⁰n, ln=b¹¹n, mn=ab²⁵, n²=b²⁶, b¹³o=ab²⁷, co=ab²o, do=b³o, eo=ab⁴o, fo=b⁵o, go=ab⁶o, ho=b⁷o, io=ab⁸o, jo=b⁹o, ko=ab¹⁰o, lo=b¹¹o, mo=ab¹²o, no=ab²⁷, o²=b²⁶, b¹³p=ab¹²o, cp=ab²p, dp=b³p, ep=ab⁴p, fp=b⁵p, gp=ab⁶p, hp=b⁷p, ip=ab⁸p, jp=b⁹p, kp=ab¹⁰p, lp=b¹¹p, mp=ab¹²p, np=ab¹²o, op=ab²⁷, p²=b²⁶, b¹²q=ab¹¹p, cq=ab²q, dq=b³q, eq=ab⁴q, fq=b⁵q, gq=ab⁶q, hq=b⁷q, iq=ab⁸q, jq=b⁹q, kq=ab¹⁰q, lq=b¹¹q, mq=b¹¹p, nq=ab¹²p, oq=ab¹²o, pq=ab²⁷, q²=b²⁶, b¹¹r=ab¹⁰q, cr=ab²r, dr=b³r, er=ab⁴r, fr=b⁵r, gr=ab⁶r, hr=b⁷r, ir=ab⁸r, jr=b⁹r, kr=ab¹⁰r, lr=ab¹⁰q, mr=b¹¹q, nr=b¹¹p, or=ab¹²p, pr=ab¹²o, qr=ab²⁷, r²=b²⁶, b¹⁰s=ab⁹r, cs=ab²s, ds=b³s, es=ab⁴s, fs=b⁵s, gs=ab⁶s, hs=b⁷s, is=ab⁸s, js=b⁹s, ks=b⁹r, ls=ab¹⁰r, ms=ab¹⁰q, ns=b¹¹q, os=b¹¹p, ps=ab¹²p, qs=ab¹²o, rs=ab²⁷, s²=b²⁶, b⁹t=ab⁸s, ct=ab²t, dt=b³t, et=ab⁴t, ft=b⁵t, gt=ab⁶t, ht=b⁷t, it=ab⁸t, jt=ab⁸s, kt=b⁹s, lt=b⁹r, mt=ab¹⁰r, nt=ab¹⁰q, ot=b¹¹q, pt=b¹¹p, qt=ab¹²p, rt=ab¹²o, st=ab²⁷, t²=b²⁶, b⁸u=ab⁷t, cu=ab²u, du=b³u, eu=ab⁴u, fu=b⁵u, gu=ab⁶u, hu=b⁷u, iu=b⁷t, ju=ab⁸t, ku=ab⁸s, lu=b⁹s, mu=b⁹r, nu=ab¹⁰r, ou=ab¹⁰q, pu=b¹¹q, qu=b¹¹p, ru=ab¹²p, su=ab¹²o, tu=ab²⁷, u²=b²⁶, b⁷v=ab⁶u, cv=ab²v, dv=b³v, ev=ab⁴v, fv=b⁵v, gv=ab⁶v, hv=ab⁶u, iv=b⁷u, jv=b⁷t, kv=ab⁸t, lv=ab⁸s, mv=b⁹s, nv=b⁹r, ov=ab¹⁰r, pv=ab¹⁰q, qv=b¹¹q, rv=b¹¹p, sv=ab¹²p, tv=ab¹²o, uv=ab²⁷, v²=b²⁶, b⁶w=ab⁵v, cw=ab²w, dw=b³w, ew=ab⁴w, fw=b⁵w, gw=b⁵v, hw=ab⁶v, iw=ab⁶u, jw=b⁷u, kw=b⁷t, lw=ab⁸t, mw=ab⁸s, nw=b⁹s, ow=b⁹r, pw=ab¹⁰r, qw=ab¹⁰q, rw=b¹¹q, sw=b¹¹p, tw=ab¹²p, uw=ab¹²o, vw=ab²⁷, w²=b²⁶, b⁵x=ab⁴w, cx=ab²x, dx=b³x, ex=ab⁴x, fx=ab⁴w, gx=b⁵w, hx=b⁵v, ix=ab⁶v, jx=ab⁶u, kx=b⁷u, lx=b⁷t, mx=ab⁸t, nx=ab⁸s, ox=b⁹s, px=b⁹r, qx=ab¹⁰r, rx=ab¹⁰q, sx=b¹¹q, tx=b¹¹p, ux=ab¹²p, vx=ab¹²o, wx=ab²⁷, x²=b²⁶, b⁴y=ab³x, cy=ab²y, dy=b³y, ey=b³x, fy=ab⁴x, gy=ab⁴w, hy=b⁵w, iy=b⁵v, jy=ab⁶v, ky=ab⁶u, ly=b⁷u, my=b⁷t, ny=ab⁸t, oy=ab⁸s, py=b⁹s, qy=b⁹r, ry=ab¹⁰r, sy=ab¹⁰q, ty=b¹¹q, uy=b¹¹p, vy=ab¹²p, wy=ab¹²o, xy=ab²⁷, y²=b²⁶, b³z=ab²y, cz=ab²z, dz=ab²y, ez=b³y, fz=b³x, gz=ab⁴x, hz=ab⁴w, iz=b⁵w, jz=b⁵v, kz=ab⁶v, lz=ab⁶u, mz=b⁷u, nz=b⁷t, oz=ab⁸t, pz=ab⁸s, qz=b⁹s, rz=b⁹r, sz=ab¹⁰r, tz=ab¹⁰q, uz=b¹¹q, vz=b¹¹p, wz=ab¹²p, xz=ab¹²o, yz=ab²⁷, z²=b²⁶, b³A=bz, cA=ab²A, dA=bz, eA=ab²z, fA=ab²y, gA=b³y, hA=b³x, iA=ab⁴x, jA=ab⁴w, kA=b⁵w, lA=b⁵v, mA=ab⁶v, nA=ab⁶u, oA=b⁷u, pA=b⁷t, qA=ab⁸t, rA=ab⁸s, sA=b⁹s, tA=b⁹r, uA=ab¹⁰r, vA=ab¹⁰q, wA=b¹¹q, xA=b¹¹p, yA=ab¹²p, zA=ab¹²o, A²=b²⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², b²⁴, b²⁶, ad, be, af, ab²f, bg, b³g, ah, ab²h, ab⁴h, bi, b³i, b⁵i, aj, ab²j, ab⁴j, ab⁶j, bk, b³k, b⁵k, b⁷k, al, ab²l, ab⁴l, ab⁶l, ab⁸l, bm, b³m, b⁵m, b⁷m, b⁹m, an, ab²n, ab⁴n, ab⁶n, ab⁸n, ab¹⁰n, bo, b³o, b⁵o, b⁷o, b⁹o, b¹¹o, ap, ab²p, ab⁴p, ab⁶p, ab⁸p, ab¹⁰p, ab¹²p, bq, b³q, b⁵q, b⁷q, b⁹q, b¹¹q, ar, ab²r, ab⁴r, ab⁶r, ab⁸r, ab¹⁰r, bs, b³s, b⁵s, b⁷s, b⁹s, at, ab²t, ab⁴t, ab⁶t, ab⁸t, bu, b³u, b⁵u, b⁷u, av, ab²v, ab⁴v, ab⁶v, bw, b³w, b⁵w, ax, ab²x, ab⁴x, by, b³y, az, ab²z, aA, ab²A}

Phi = 1 a b a b c b c b³ c d abd d e abe e f abf f g abg g h abh h i abi i j abj j k abk k l abl l m abm m n abn n o abo o p abp p q abq q r abr r s abs s t abt t u abu u v abv v w abw w x abx x y aby y z abz z abA b²A abA A abA A

Monoid Structure