Details Page for 0.3072

Complete Solution is Known:

MSV File: q-0.3072.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₁₀(0.3072):

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, b²c=ab⁴, c²=b⁴, b²d=ab⁶, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b²f=ab⁷, ef=abdf, f²=b¹⁰, b²g=bcf, cg=abcf, dg=ab¹⁰, eg=b¹¹, fg=ab¹¹, g²=b¹², b³h=abdf, ch=ab²h, dh=b¹¹, eh=ab¹², fh=b¹², gh=ab¹³, h²=b¹⁴, b⁵i=b¹³, ci=ab²i, di=ab⁴i, ei=b¹³, fi=ab¹³, gi=b¹⁴, hi=ab¹⁵, i²=b¹⁶, b⁶j=ab¹⁵, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁵j, gj=ab¹⁵, hj=b¹⁶, ij=ab¹⁷, j²=b¹⁸, b⁷k=b¹⁷, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁵k, gk=b⁶k, hk=ab¹⁷, ik=b¹⁸, jk=ab¹⁹, k²=b²⁰, b⁸l=ab¹⁹, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁵l, gl=b⁶l, hl=ab⁷l, il=ab¹⁹, jl=b²⁰, kl=ab²¹, l²=b²², b⁹m=b²¹, cm=ab²m, dm=ab⁴m, em=b⁵m, fm=ab⁵m, gm=b⁶m, hm=ab⁷m, im=b⁸m, jm=ab²¹, km=b²², lm=ab²³, m²=b²², b¹⁰n=ab²³, cn=ab²n, dn=ab⁴n, en=b⁵n, fn=ab⁵n, gn=b⁶n, hn=ab⁷n, in=b⁸n, jn=ab⁹n, kn=ab²³, ln=b²², mn=ab²³, n²=b²², b¹⁰o=ab⁹n, co=ab²o, do=ab⁴o, eo=b⁵o, fo=ab⁵o, go=b⁶o, ho=ab⁷o, io=b⁸o, jo=ab⁹o, ko=ab⁹n, lo=ab²³, mo=b²², no=ab²³, o²=b²², b⁹p=ab⁸o, cp=ab²p, dp=ab⁴p, ep=b⁵p, fp=ab⁵p, gp=b⁶p, hp=ab⁷p, ip=b⁸p, jp=b⁸o, kp=ab⁹o, lp=ab⁹n, mp=ab²³, np=b²², op=ab²³, p²=b²², b⁸q=ab⁷p, cq=ab²q, dq=ab⁴q, eq=b⁵q, fq=ab⁵q, gq=b⁶q, hq=ab⁷q, iq=ab⁷p, jq=b⁸p, kq=b⁸o, lq=ab⁹o, mq=ab⁹n, nq=ab²³, oq=b²², pq=ab²³, q²=b²², b⁷r=ab⁶q, cr=ab²r, dr=ab⁴r, er=b⁵r, fr=ab⁵r, gr=b⁶r, hr=b⁶q, ir=ab⁷q, jr=ab⁷p, kr=b⁸p, lr=b⁸o, mr=ab⁹o, nr=ab⁹n, or=ab²³, pr=b²², qr=ab²³, r²=b²², b⁶s=ab⁵r, cs=ab²s, ds=ab⁴s, es=b⁵s, fs=ab⁵s, gs=ab⁵r, hs=b⁶r, is=b⁶q, js=ab⁷q, ks=ab⁷p, ls=b⁸p, ms=b⁸o, ns=ab⁹o, os=ab⁹n, ps=ab²³, qs=b²², rs=ab²³, s²=b²², b⁵t=ab⁴s, ct=ab²t, dt=ab⁴t, et=ab⁴s, ft=b⁴s, gt=ab⁵s, ht=ab⁵r, it=b⁶r, jt=b⁶q, kt=ab⁷q, lt=ab⁷p, mt=b⁸p, nt=b⁸o, ot=ab⁹o, pt=ab⁹n, qt=ab²³, rt=b²², st=ab²³, t²=b²², b⁴u=ab³t, cu=ab²u, du=b³t, eu=ab⁴t, fu=b⁴t, gu=b⁴s, hu=ab⁵s, iu=ab⁵r, ju=b⁶r, ku=b⁶q, lu=ab⁷q, mu=ab⁷p, nu=b⁸p, ou=b⁸o, pu=ab⁹o, qu=ab⁹n, ru=ab²³, su=b²², tu=ab²³, u²=b²², b³v=ab²u, cv=ab²v, dv=b³u, ev=b³t, fv=ab³t, gv=b⁴t, hv=b⁴s, iv=ab⁵s, jv=ab⁵r, kv=b⁶r, lv=b⁶q, mv=ab⁷q, nv=ab⁷p, ov=b⁸p, pv=b⁸o, qv=ab⁹o, rv=ab⁹n, sv=ab²³, tv=b²², uv=ab²³, v²=b²², b²w=abv, cw=bv, dw=ab²u, ew=b³u, fw=ab³u, gw=ab³t, hw=b⁴t, iw=b⁴s, jw=ab⁵s, kw=ab⁵r, lw=b⁶r, mw=b⁶q, nw=ab⁷q, ow=ab⁷p, pw=b⁸p, qw=b⁸o, rw=ab⁹o, sw=ab⁹n, tw=ab²³, uw=b²², vw=ab²³, w²=b²², bx=aw, cx=bw, dx=ab²v, ex=ab²u, fx=b²u, gx=ab³u, hx=ab³t, ix=b⁴t, jx=b⁴s, kx=ab⁵s, lx=ab⁵r, mx=b⁶r, nx=b⁶q, ox=ab⁷q, px=ab⁷p, qx=b⁸p, rx=b⁸o, sx=ab⁹o, tx=ab⁹n, ux=ab²³, vx=b²², wx=ab²³, x²=b²², b²y=x, cy=ax, dy=bw, ey=bv, fy=abv, gy=b²v, hy=b²u, iy=ab³u, jy=ab³t, ky=b⁴t, ly=b⁴s, my=ab⁵s, ny=ab⁵r, oy=b⁶r, py=b⁶q, qy=ab⁷q, ry=ab⁷p, sy=b⁸p, ty=b⁸o, uy=ab⁹o, vy=ab⁹n, wy=ab²³, xy=b²², y²=b²²>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, b¹⁸, b²⁰, b²², ae, bf, abg, h, b²h, abi, ab³i, j, b²j, b⁴j, abk, ab³k, ab⁵k, l, b²l, b⁴l, b⁶l, abm, ab³m, ab⁵m, ab⁷m, n, b²n, b⁴n, b⁶n, b⁸n, abo, ab³o, ab⁵o, ab⁷o, ab⁹o, p, b²p, b⁴p, b⁶p, b⁸p, abq, ab³q, ab⁵q, ab⁷q, r, b²r, b⁴r, b⁶r, abs, ab³s, ab⁵s, t, b²t, b⁴t, abu, ab³u, v, b²v, abw, x, y}

Phi = 1 a 1 a 1 b ab b ab a 1 a 1 b ab b ab c ac c b² abc bc abc ab³ d ad d b⁴ e ae e f abe g abe b⁶ bg h bg ab⁷ bh i bh b⁸ bi j bi ab⁹ bj k bj b¹⁰ bk l bk ab¹¹ bl m bl b¹² bm n bm ab¹³ bn o bn b¹⁴ bo p bo ab¹⁵ bp q bp b¹⁶ bq r bq ab¹⁷ br s br b¹⁸ bs t bs ab¹⁹ bt u bt b²⁰ bu v bu ab²¹ bv w bv b²² bw x bw ab²³ aw aby aw b²² ax y ax ab²³ by

Monoid Structure