Details Page for 0.3506

Complete Solution is Known:

MSV File: q-0.3506.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₁₉(0.3506):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n | a²=1, b³=b, b²c=c, c³=ac², b²d=d, c²d=abc², d²=b², b²e=e, c²e=bc², e²=c², c²f=abc², cef=c², b²f²=f², cf²=ac², f³=acf, b²g=g, cg=bcde, eg=ac², g²=c², b²h=h, cdh=abch, cfh=aceh, defh=abefh, f²h=ach, gh=bdeh, c²h²=c², dfh²=abfh², ch³=ch, eh³=eh, h⁴=h², b²i=i, c²i=ac²h, cdi=abci, cei=aceh, cfi=ceh, efi=aefh, gi=bdei, chi=ach², fhi=afh², h³i=hi, f²i²=aci², hi²=ah²i, ci³=ci, i⁴=i², b²j=j, c²j=c²h, chj=ch², efhj=efh², fh²j=fh³, cij=aci², hij=h²i, fi²j=afi³, ehj²=eh²j, h²j²=h³j, eij²=ei, cej³=cej, i²j³=i²j, cfj⁴=cfj², ef²j⁴=ef²j², f²gj⁴=f²gj², hj⁴=hj², ij⁴=ij², cj⁵=cj³, ej⁵=ej³, f²j⁵=f²j³, gj⁵=gj³, j⁶=j⁴, b²k=k, ck=abc², ek=c², fk=ac², gk=ac², h³k=hk, hj²k=h²jk, ij²k=ik, j⁵k=j³k, k²=c², b²l=l, cl=bdf²i, f²l=abdf²i, fgl=aefl, hl=ah², eil=aehi, dfil=abfil, i³l=il, ijl=ai²l, ej⁴l=ej²l, gj⁴l=gj²l, j⁵l=j³l, ikl=ahik, jkl=ahjk, dfl²=abfl², gl²=bdel², il²=i²l, efj²l²=efl², j³l²=jl², efl³=aefjl², jl³=aj²l², kl³=kl, l⁴=l², b²m=m, c²m=bc²h, cdm=abcm, cem=bceh, cfm=abceh, efm=befh, df²m=abf²m, gm=bdem, hm=adh², cim=abch², eim=adehi, f²im=bch², i³m=im, fijm=afi²m, cj²m=cm, ij²m=ai²jm, j⁴m=j²m, ikm=adhik, j³km=jkm, lm=dh², cm²=bcjm, f²m²=abcjm, im²=di²m, fj²m²=fm², fm³=adfjm², ejm³=ejm, km³=km, m⁴=m², b²n=n, c²n=abc²h, chn=abch², dehn=abehn, efhn=abefh², fh²n=abfh³, cin=bci², fi²n=adfi³, cejn=abceh², ef²jn=cfjn, f²gjn=acfjn, i²j²n=i²n, dhkn=abhkn, hikn=c²h, gln=aeln, filn=bfi²l, dkln=abkln, del²n=abel²n, fl²n=bfl³, cmn=abcjm, fimn=adfi²m, ijmn=ai²mn, dej²mn=abej²mn, dkmn=abkmn, fm²n=dfjm², em³n=emn, cdfn²=abcfn², f²gn²=bdef²n², dhn²=abhn², ehn²=abeh²n, df²in²=abf²in², cfj²n²=aceh², f²j²n²=acj²n², hj²n²=h²jn², fij²n²=fi³, hkn²=abh²kn, dln²=abln², ej²ln²=bej²l²n, fj³ln²=afj²l², kln²=bkl²n, el²n²=bel³n, jl²n²=aj⁴ln², fj²mn²=adfjm², j²m³n²=j²mn², cen³=cen, fgn³=bdefn³, h²n³=abh³n², ein³=ein, hin³=abh²in², efj³n³=defj⁴n², ikn³=ikn, iln³=bi²ln², j³ln³=abj⁴ln², l²n³=bl³n², imn³=adi²mn², dejmn³=abejmn³, ej³mn³=ejmn³, j³m²n³=jm²n³, jm³n³=j³mn³, cfn⁴=cfn², efn⁴=efn², hn⁴=hn², in⁴=in², cj³n⁴=cdj⁴n³, fj⁴n⁴=dfj⁵n³, ln⁴=ln², emn⁴=aem²n³, fmn⁴=fmn², kmn⁴=akm²n³, cn⁵=cn³, f²n⁵=f²n³, gn⁵=gn³, kn⁵=kn³, j²mn⁵=aj²m²n⁴, m²n⁵=am³n⁴, n⁶=n⁴>

P = {a, b², bc, c², abd, acd, abe, de, f, abf², df², bg, adg, ah, bdh, abeh, deh, bfh, adfh, ah², bch², dh², abeh², fh², ah³, bdh³, bfh³, aci, ei, abdei, afi, dfi, f²i, abdf²i, hi, adhi, behi, h²i, abdh²i, ai², bci², di², abei², fi², abdfi², i³, adi³, abdei³, afi³, dfi³, aj, cj, bdj, acdj, abej, dej, abcdej, fj, acfj, adfj, bcdfj, befj, abdefj, af²j, df²j, bdef²j, bgj, adgj, afgj, dfgj, f²gj, ahj, bdhj, abehj, dehj, fhj, abdfhj, ah²j, bdh²j, abeh²j, deh²j, ah³j, bdh³j, bij, adij, afij, bdfij, bf²ij, adf²ij, ai²j, bdi²j, bi³j, adi³j, j², bcj², acdj², abej², dej², abf²j², df²j², bgj², adgj², ahj², bdhj², bfhj², adfhj², bij², afij², dfij², f²ij², abdf²ij², ai²j², di²j², i³j², adi³j², aj³, cj³, bdj³, acdj³, abej³, dej³, fj³, acfj³, adfj³, bcdfj³, befj³, abdefj³, af²j³, df²j³, bdef²j³, bgj³, adgj³, afgj³, dfgj³, f²gj³, ahj³, bdhj³, fhj³, abdfhj³, bij³, adij³, afij³, bdfij³, bf²ij³, adf²ij³, j⁴, bcj⁴, acdj⁴, abej⁴, dej⁴, abf²j⁴, df²j⁴, bgj⁴, adgj⁴, aj⁵, bdj⁵, fj⁵, adfj⁵, bh²k, abhik, bi²k, abijk, dijk, abi³jk, di³jk, l, abdl, bel, adel, abfl, dfl, aefl, bdefl, abgl, dgl, ail, dil, fil, i²l, abdi²l, abfi²l, jl, abdjl, bejl, adejl, abgjl, dgjl, j²l, abdj²l, bej²l, adej²l, abfj²l, dfj²l, aefj²l, bdefj²l, abgj²l, dgj²l, j³l, abdj³l, bej³l, adej³l, abgj³l, dgj³l, j⁴l, abdj⁴l, abfj⁴l, dfj⁴l, al², dl², abel², fl², ajl², bdjl², abejl², dejl², bfjl², efjl², aj²l², bdj²l², abej²l², dej²l², bkl², l³, abdl³, bel³, adel³, abfl³, abm, cm, dm, aem, bdem, fm, adfm, af²m, im, adim, abfim, dfim, ai²m, di²m, fi²m, adfi²m, abjm, cjm, djm, aejm, bdejm, bfjm, adfjm, af²jm, bijm, adijm, ai²jm, di²jm, abj²m, dj²m, aej²m, bdej²m, fj²m, adfj²m, af²j²m, abj³m, dj³m, aej³m, bdej³m, bfj³m, adfj³m, af²j³m, am², dm², abem², fm², abdfm², ajm², bdjm², abejm², dejm², fjm², adfjm², aj²m², bdj²m², abej²m², dej²m², aj³m², bdj³m², abej³m², dej³m², bkm², am³, dm³, bdem³, abjm³, djm³, abj²m³, dj²m³, abj³m³, dj³m³, n, acn, abdn, cdn, ben, aden, bcden, afn, cfn, dfn, abcdfn, abefn, bdefn, f²n, adf²n, abdef²n, abgn, dgn, fgn, adfgn, af²gn, hn, abdhn, abfhn, dfhn, bh²n, eh²n, h³n, abdh³n, aein, bdein, bfin, adfin, af²in, bdf²in, abhin, ah²in, bdh²in, i²n, abdi²n, bei²n, adei²n, bdi³n, aei³n, ejn, abdejn, acfjn, bcdfjn, agjn, bdgjn, ehjn, eh²jn, abijn, dijn, fijn, abdfijn, i²jn, abdi²jn, abi³jn, di³jn, acj²n, bcdj²n, ej²n, adej²n, afj²n, dfj²n, bdefj²n, f²j²n, abdf²j²n, agj²n, dgj²n, fgj²n, abfhj²n, dfhj²n, bfij²n, adfij²n, af²ij²n, bdf²ij²n, bcdj³n, ej³n, abdej³n, abfj³n, acfj³n, abdf²j³n, agj³n, bdgj³n, bdfhj³n, abij³n, dij³n, fij³n, abdfij³n, df²ij³n, acj⁴n, cdj⁴n, ej⁴n, adej⁴n, afj⁴n, dfj⁴n, bdefj⁴n, f²j⁴n, adf²j⁴n, agj⁴n, dgj⁴n, fgj⁴n, adfgj⁴n, abfj⁵n, ahkn, i³kn, ai²jkn, bdi²jkn, aeln, bdeln, bfln, adfln, biln, ai²ln, bdi²ln, aejln, bdejln, fjln, abdfjln, aej²ln, bdej²ln, bfj²ln, adfj²ln, aej³ln, bdej³ln, fj³ln, abdfj³ln, befj³ln, adfj⁴ln, bl²n, el²n, ejl²n, ej²l²n, ael³n, bmn, admn, afmn, bdfmn, bf²mn, abimn, dimn, bi²mn, adi²mn, bjmn, adjmn, afjmn, bdfjmn, bj²mn, adj²mn, afj²mn, bdfj²mn, bf²j²mn, bj³mn, adj³mn, afj³mn, bdfj³mn, abkmn, abj²kmn, m²n, abdm²n, jm²n, abdjm²n, j²m²n, abdj²m²n, j³m²n, abdj³m²n, ajkm²n, bm³n, adm³n, bjm³n, adjm³n, bj²m³n, adj²m³n, bj³m³n, adj³m³n, bcn², abdn², acdn², aben², den², abf²n², df²n², bgn², adgn², ahn², bfhn², abh²n², ah³n², adin², ein², abdein², afin², dfin², f²in², bhin², h²in², abei²n², dei²n², i³n², adi³n², abdei³n², cjn², abcdjn², aejn², dejn², fjn², adfjn², abdefjn², af²jn², bdf²jn², gjn², adgjn², afgjn², fhjn², bijn², adijn², afijn², bdfijn², bf²ijn², ai²jn², bdi²jn², bi³jn², adi³jn², abj²n², bcj²n², acdj²n², dej²n², bgj²n², bij²n², adij²n², cj³n², abcdj³n², aej³n², dej³n², fj³n², adfj³n², befj³n², abdefj³n², gj³n², adgj³n², afgj³n², bij³n², adij³n², abj⁴n², bcj⁴n², acdj⁴n², dej⁴n², bgj⁴n², fj⁵n², adfj⁵n², abijkn², dijkn², abi³jkn², di³jkn², adj²kn², adj⁴kn², beln², abfln², aefln², abiln², i²ln², bejln², abfj²ln², amn², dmn², bdemn², fmn², adfmn², af²mn², imn², abdimn², ai²mn², di²mn², aejmn², bdejmn², bfjmn², adfjmn², af²jmn², abj²mn², dj²mn², aej²mn², aej³mn², abm²n², dm²n², ajm²n², djm²n², abejm²n², abej²m²n², aj³m²n², bdj³m²n², abej³m²n², bkm²n², am³n², dm³n², n³, acn³, abdn³, cdn³, ben³, aden³, afn³, cfn³, dfn³, abefn³, bdefn³, f²n³, adf²n³, abdef²n³, abgn³, dgn³, hn³, abfhn³, bfin³, adfin³, af²in³, i²n³, abdi²n³, bdi³n³, ejn³, abdejn³, acfjn³, agjn³, bdgjn³, abijn³, dijn³, fijn³, abdfijn³, i²jn³, abdi²jn³, abi³jn³, di³jn³, acj²n³, adj²n³, bcdj²n³, ej²n³, abdej²n³, afj²n³, dfj²n³, bdefj²n³, agj²n³, dgj²n³, acj³n³, bcdj³n³, ej³n³, abdej³n³, abfj³n³, dfj³n³, agj³n³, bdgj³n³, abij³n³, dij³n³, acj⁴n³, adj⁴n³, cdj⁴n³, ej⁴n³, abdej⁴n³, afj⁴n³, dfj⁴n³, agj⁴n³, dgj⁴n³, aeln³, bfln³, aejln³, fjln³, bfj²ln³, bmn³, admn³, afmn³, bdfmn³, bf²mn³, bjmn³, adjmn³, afjmn³, bdfjmn³, bj²mn³, adj²mn³, bj³mn³, adj³mn³, abkmn³, abj²kmn³, m²n³, adm²n³, abdem²n³, ejm²n³, ej²m²n³, bm³n³, adm³n³, bcn⁴, abdn⁴, acdn⁴, aben⁴, den⁴, abf²n⁴, df²n⁴, bgn⁴, adgn⁴, cjn⁴, abcdjn⁴, aejn⁴, dejn⁴, fjn⁴, adfjn⁴, af²jn⁴, bdf²jn⁴, gjn⁴, adgjn⁴, abj²n⁴, bcj²n⁴, acdj²n⁴, dej²n⁴, bgj²n⁴, aej³n⁴, dej³n⁴, fj³n⁴, adfj³n⁴, gj³n⁴, adgj³n⁴, abej⁴n⁴, dej⁴n⁴, bgj⁴n⁴, adgj⁴n⁴, adj²kn⁴, amn⁴, dmn⁴, abj²mn⁴, dj²mn⁴, abm²n⁴, dm²n⁴, abjm²n⁴, djm²n⁴, abj²m²n⁴, dj²m²n⁴, am³n⁴, dm³n⁴, n⁵, abdn⁵, ben⁵, aden⁵, afn⁵, dfn⁵, ejn⁵, abdejn⁵, adj²n⁵, ej²n⁵, abdej²n⁵, afj²n⁵, dfj²n⁵, ej³n⁵, abdej³n⁵, abfj³n⁵, ej⁴n⁵, adej⁴n⁵, bmn⁵, admn⁵, bjmn⁵, adjmn⁵}

Phi = 1 a b c² c 1 d ac² e f ad c² g h i j k l m n

Monoid Structure