Details Page for 0.5135

Complete Solution is Known:

MSV File: q-0.5135.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₂(0.5135):

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 | a²=1, b²⁴=b²², bc=ab³, c²=b⁴, bd=ab⁵, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b³f=ab⁹, cf=ab²f, df=b¹⁰, ef=ab¹¹, f²=b¹², b⁴g=b¹¹, cg=ab²g, dg=ab¹¹, eg=b¹², fg=ab¹³, g²=b¹⁴, b⁵h=ab¹³, ch=ab²h, dh=ab⁴h, eh=ab¹³, fh=b¹⁴, gh=ab¹⁵, h²=b¹⁶, b⁶i=b¹⁵, ci=ab²i, di=ab⁴i, ei=b⁵i, fi=ab¹⁵, gi=b¹⁶, hi=ab¹⁷, i²=b¹⁸, b⁷j=ab¹⁷, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁶j, gj=ab¹⁷, hj=b¹⁸, ij=ab¹⁹, j²=b²⁰, b⁸k=b¹⁹, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁶k, gk=b⁷k, hk=ab¹⁹, ik=b²⁰, jk=ab²¹, k²=b²², b⁹l=ab²¹, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁶l, gl=b⁷l, hl=ab⁸l, il=ab²¹, jl=b²², kl=ab²³, l²=b²², b¹⁰m=b²³, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁶m, gm=b⁷m, hm=ab⁸m, im=b⁹m, jm=ab²³, km=b²², lm=ab²³, m²=b²², b¹⁰n=ab⁹m, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁶n, gn=b⁷n, hn=ab⁸n, in=b⁹n, jn=b⁹m, kn=ab²³, ln=b²², mn=ab²³, n²=b²², b⁹o=ab⁸n, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁶o, go=b⁷o, ho=ab⁸o, io=ab⁸n, jo=b⁹n, ko=b⁹m, lo=ab²³, mo=b²², no=ab²³, o²=b²², b⁸p=ab⁷o, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁶p, gp=b⁷p, hp=b⁷o, ip=ab⁸o, jp=ab⁸n, kp=b⁹n, lp=b⁹m, mp=ab²³, np=b²², op=ab²³, p²=b²², b⁷q=ab⁶p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁶q, gq=ab⁶p, hq=b⁷p, iq=b⁷o, jq=ab⁸o, kq=ab⁸n, lq=b⁹n, mq=b⁹m, nq=ab²³, oq=b²², pq=ab²³, q²=b²², b⁶r=ab⁵q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=b⁵q, gr=ab⁶q, hr=ab⁶p, ir=b⁷p, jr=b⁷o, kr=ab⁸o, lr=ab⁸n, mr=b⁹n, nr=b⁹m, or=ab²³, pr=b²², qr=ab²³, r²=b²², b⁵s=ab⁴r, cs=ab²s, ds=ab⁴s, es=ab⁴r, fs=b⁵r, gs=b⁵q, hs=ab⁶q, is=ab⁶p, js=b⁷p, ks=b⁷o, ls=ab⁸o, ms=ab⁸n, ns=b⁹n, os=b⁹m, ps=ab²³, qs=b²², rs=ab²³, s²=b²², b⁴t=ab³s, ct=ab²t, dt=b³s, et=ab⁴s, ft=ab⁴r, gt=b⁵r, ht=b⁵q, it=ab⁶q, jt=ab⁶p, kt=b⁷p, lt=b⁷o, mt=ab⁸o, nt=ab⁸n, ot=b⁹n, pt=b⁹m, qt=ab²³, rt=b²², st=ab²³, t²=b²², b³u=ab²t, cu=ab²u, du=b³t, eu=b³s, fu=ab⁴s, gu=ab⁴r, hu=b⁵r, iu=b⁵q, ju=ab⁶q, ku=ab⁶p, lu=b⁷p, mu=b⁷o, nu=ab⁸o, ou=ab⁸n, pu=b⁹n, qu=b⁹m, ru=ab²³, su=b²², tu=ab²³, u²=b²², b²v=abu, cv=bu, dv=ab²t, ev=b³t, fv=b³s, gv=ab⁴s, hv=ab⁴r, iv=b⁵r, jv=b⁵q, kv=ab⁶q, lv=ab⁶p, mv=b⁷p, nv=b⁷o, ov=ab⁸o, pv=ab⁸n, qv=b⁹n, rv=b⁹m, sv=ab²³, tv=b²², uv=ab²³, v²=b²², bw=av, cw=bv, dw=ab²u, ew=ab²t, fw=b³t, gw=b³s, hw=ab⁴s, iw=ab⁴r, jw=b⁵r, kw=b⁵q, lw=ab⁶q, mw=ab⁶p, nw=b⁷p, ow=b⁷o, pw=ab⁸o, qw=ab⁸n, rw=b⁹n, sw=b⁹m, tw=ab²³, uw=b²², vw=ab²³, w²=b²², bx=aw, cx=av, dx=bu, ex=ab²u, fx=ab²t, gx=b³t, hx=b³s, ix=ab⁴s, jx=ab⁴r, kx=b⁵r, lx=b⁵q, mx=ab⁶q, nx=ab⁶p, ox=b⁷p, px=b⁷o, qx=ab⁸o, rx=ab⁸n, sx=b⁹n, tx=b⁹m, ux=ab²³, vx=b²², wx=ab²³, x²=b²², by=ax, cy=aw, dy=bv, ey=bu, fy=ab²u, gy=ab²t, hy=b³t, iy=b³s, jy=ab⁴s, ky=ab⁴r, ly=b⁵r, my=b⁵q, ny=ab⁶q, oy=ab⁶p, py=b⁷p, qy=b⁷o, ry=ab⁸o, sy=ab⁸n, ty=b⁹n, uy=b⁹m, vy=ab²³, wy=b²², xy=ab²³, y²=b²²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², ae, bf, ag, ab²g, bh, b³h, ai, ab²i, ab⁴i, bj, b³j, b⁵j, ak, ab²k, ab⁴k, ab⁶k, bl, b³l, b⁵l, b⁷l, am, ab²m, ab⁴m, ab⁶m, ab⁸m, bn, b³n, b⁵n, b⁷n, b⁹n, ao, ab²o, ab⁴o, ab⁶o, ab⁸o, bp, b³p, b⁵p, b⁷p, aq, ab²q, ab⁴q, ab⁶q, br, b³r, b⁵r, as, ab²s, ab⁴s, bt, b³t, au, ab²u, bv, aw, ay}

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

Monoid Structure