iliiw zgqep a"dx`,mit,(daniel J. Kleitman),onhiilw l`ipc 'text oeipkha ihnznd oecrena dpzipy d`vxd opeazp ep`.mipey micewcew ly bef `id rlv lk.zerlv zerlvde,micewcew micewcewd :zeveaw izyn akxen sxb zxne` z`f,zepeekn zerlv yi oeekn sxbl.micewcewd zveaw ixa` xtqn n idie,miiteq mitxba.dly apfd `ed ipyde rlvd ly y`x y`xd `ed cg`,micewcew ly xceqn bef `id rlv :y jk zerlv ly dniyx `ed y cewcewl x cewcewdn sxba lelqn ;y z` dlikn dpexg`d rlvde x z` dlikn dpey`xd rlvd rlvd mr szeyn xg` cewcewe,dl zawerd rlvd mr szeyn cewcew yi dniyxa rlv lkl.dl zncewd lcgiy xiyw sxb `ed ur.ea xg` cewcew lkl cewcew lkn lelqn yi m` xiyw `xwp sxb.ely rlv idyefi` epnn e`ivei m` xiyw zeidl miwela n n akxen sxbde ccean `ed cewcew lk if` zerlv oi` G sxbl m` :zerlv n yi url) miwela ipy zxagn e` G l ztqepy rlv lk.cg` cewcewn akxen mdn cg` lky mixf mixiyw dhinydl xyt` df dxwnae,miiw wela jeza z`vnp e`,cg`a miwelad xtqn z` dpihwn jkae `ll sxbl zexiywl-zeigxkd zerlv n ztqed ixg`,jk m`.zexiywd z` lwlwl ila G n (.xiywl jtdii `ed,zerlv.xzeid lkl eay zerlvdn mizya xg` cewcew lk likny envrl cewcewn lelqn `ed lbrn.zexiywd zcin z` oihwdl ila rlv hinydl xyt` lbrnn :milbrn oi` ura n = 6 sxb ur lbrn dveaw mr yi mipey mivr dnk :d`ad dl`yd lr dpre l`y (Cayley) iliiw,dxyr-ryzd d`na `idy dgked o`k mibivn ep`.ely d`vezd ly zeax zegked erited f`n?micewcew n ly dpezp.dycg ile`
daxnl :miphwd mixwnd z` wecap jk zeyrl ick :daeyzd z` ygpl lkep m` mcew d`xp mivr dnk xetql xyt`e,url zeidl zelekiy zexev hrn wx yi n ly miphw mikxr xear,lfnd.`ad xeiva dyrp df.ax iyew `ll dxev lkn yi icewcewl `exwl") mipezpd micewcewd n zveaw lr dxev icewcew z` miyl xyt` llk jxca d`ixw"n lawzi ur eze` if`,dixhniq yi dxevl m`,la`.mipey mipte` n! a ("zenya dxevd dxev lkn mipeyd mivrd xtqn z` `evnl ick.dixhniq zlert i"r dzpenzne "zenya idylk dixhniqd zxeag xcqa,zexg` milna) dxevl yiy dixhniqd zelert xtqna n! z` wlgl yi.(dly!/=!/!=!/=!/!=!/=60!/=60 n n = n = n = 6 n = mivrd 'qn `ian dfe,c() =,c() =,c() = :micewcew n lr c(n) mivrd xtqn xear,mi`ven.c() = = 0 :n = xear elit` lret df.c(n) = n n `id daeyzdy dxrydl :zeixyt`d zexevd zex`ezn xeiva :n = 6 z` wecap n = 6 xear zexevd 6!/!=6 6!/!=0 6!/=60 6!/=60 6!/8=90 60 + 90 + 0 + 6 = 96 = 6 6 6 6 6!/=60.n n `id zillkd daeyzdy mirpkeyn xak i`ceea mz`,(iliiw enke) ipenk mz` m`?dpen n n,dfd xtqndy mircei ep` dn :mcew l`yp,z`f zeyrl ick.gikepy dn df, = ( + + + ) ( + + + ), = ( + + ) y d`xp,miphw mixwn aey wecap m`.mi- n mekq `ed mdn cg` lky midf minxeb n ly dltkn `ed n n illk ote`ae
miktedy cr mrt xg` mrt ef dltkn iabl (belitd weg) iaiheaixhqicd wega ynzydl xyt` lk, `ed dfk xai` lky oeik.miixewnd minxebdn miccea mixa` ly zeltkn ly mekql dze` weg zlrtdn milawzny mipeyd mixa`d xtqn `ed eply n n e, l zeey eidi dl`d zeltknd.o`k belitd minrt n,zeiexyt` n oian zg` zexyt` xegal zepeyd mikxcd xtqn z` dpen n n okl.zelcap.mivrd xtqn z` mb dpen xtqn eze`y gikedle,jka ynzydl mivex ep` :epzgked ly daygnd jxc didz ef.miixbeqa mi- inekq ly dltknk azkidl leki n n."divwpet" i"r xe`izl ozip miixbeqd zgizt ixg` lawzny xai` lk.oeekn sxb zraew efk divwpet lk.dfk ote`a milawzn mivrd lke mieqn url mi`zn dfk oeekn sxb lk.mivrd xtqn `ed n n okl ly dxiga deedn xai` :`ad ote`a divwpetl belitd weg itl dltknd gezita xai` mikted ep` mi`zn xai` lk if`,,,..., n zeny mipeyd zenewnl ozip m`.miixbeqdn cg` lka cg` mewn.xai`l dni`zny divwpetd idef.miixbeqdn cg` lkl dl` miirah mixtqnn cg` zn`zdl = ( + + + + )( + + + + )( + + + + ).n = mr dnbec dpd.f() =, f() =, f() = dn`zdd e` "divwpet"d i"r x`zl xyt` miybcend mixai`d z`.zxg` divwpet i"r x`ezn dltknd gezita xai` lke,lynl,f() = dcaerd z` miyxtny jk i"r efk divwpetl mi`zny oeekn sxb zepal xyt`. l n zpeekn rlv meiw xeza :lirl xai`dn d`ay divwpetl mi`zny oeeknd sxbd,`eti`,edf f() =, f() =, f() = mpi` mivry cera mipeekn mitxb dl`,lynl.mivr mpi` z`fk dxeva milawn ep`y mitxbd.mipeekn jtdp ur lk f`.n cewcewd l` epeekziy jk ur lka zerlvd z` oeekl xyt` :owzl lw df z`.eply mitxbd enk d`xp `l oiicr df la` ;oeekn sxbl
6 7 ur 6 n = 7,n oeeikl zepeekn zerlv mr ur mdn cg` lka :mipte` dyelya eply mitxbdn milcap md,dfk ote`a mivrl miqgiizn xy`k mileki eply mitxbay cera,milbrn mda oi` ;oi` eply mitxbay cera,n n z`veiy rlv yi zeidl zaiig `l eply mitxba ;n l zpeekn rlv yi,df ote`a oeeknd,ur lka,jkl sqepa.zeidl 7.efk rlv lk jxc xaery,n l n n lelqn xevip,g dfk sxb oezp :url eply mitxbdn cg` lk jetdp jk.epxnb f`,ikxr-cg ote`a jildzd z` (lhal) jetdl mb mileki ep` m`.eze` qxede G a lbrn ixtqnd qwcpi`dy cewcewd xnelk) mda xzeia lecbd cewcewd itl milbrnd z` xcqp?ji` qpkidle n a ligzdl eply lelqnl ozip ;dligz xzeia lecbd,(xzeia lecbd `ed,,..., n :ely l`,xzei oi` m`,e`) `ad lbrnd l` z`vle,lbrna xzeia lecbd cewcewd ixg` ciin lbrn lkl zrk.(lbrna el awerd l` xzeia lecbd cewcewdn rlvd hnyiz jkae) xzeia lecbd cewcewa (n.milbrn xzei oi`y cr,dipad lr mixfege elceba ipyd cewcewd lra lbrnl mixaer ep` f() =, f() =, f() = n = ADD OMIT :dyrp df cvik dnbec dpd ADD :url jetdl ick {, } :lbrna xzeia lecbd ixg`y cewcewl n n rlv sqed {, } :n l` e` `ad lbrnd l` lbrna xzeia lecbdn rlv sqed {, } :xzeia lecbd cewcewdn z`veid lbrna rlvd z` hnyd l n n lelqnd z` `vn,t mi`znd urdn G z` lawl ick - dipad z` (lhal) jetdl ick lbrn ycgn dpa.g a oey`xd lbrnd dvw z` onqn df lelqna xzeia lecbd cewcewd ;T a n cr jynde,dnec ote`a ycgn eze` dpa ;`ad lbrnl xeare,n n z`veiy rlvd z` hnyd,df.g z` zxviy
in T\G in G\T in T\G.lbrna xzeia lecbd cewcewdn z`veiy ef - lbrn lkn rlvn akxen G \ T awerd l` lbrn lka xzeia lecbd cewcewdn zerlv,oey`xd lbrnl n n rlvn akxen T \ G.n l` rlv seqale,`ad lbrna xzeia lecbl xiivl eqp,milret dl` milewiyy mknvr z` rpkyl mivex mz` m`.iliiw zgqep z` epgked.dketdd jxca mb zklle n n ly gezita mixai`le zeivwpetl,mitxbl mze` jetdle mivr dnk mifexg mr zfexgn ziiyr il xikfn o`k z`f miyer ep`y enk lelqna milbrn zxnd ly jildzd.lcebd itl mixceqn wegd) belitd weg itl dze` migztn xy`k,(x + x + + x n ) n divwpetd :ztqep :ztqep dxrd enk weica,ur lk xear cg` okle,g sxb lk xear cg`,mixai` n n n zakxen,(iaiheaixhqicd gwlp j m` x j k dwfg yi miieqn ur i"r mxzpy xai`a. mlek mpi` mixai`dy jkl hxt,lirl G a j cewcewd ly zqpkpd zeikxrdy xne` df ;belitd wegn mi`znd xai`d ziipaa minrt k.k `id divwpetd okl ;G a cewcew eze` ly zqpkpd zeikxrdn xzei a weica `id T a zeikxr lk `idy dwfgl dlren x j ly n e oia j miqwcpi` xear dltknd ly mivrd lr mekqd `id lirl :jk azkp df ihnzn oeniqa. zegt T a j cewcewd zeikxr n ( (xj ) ) d j(t ) j=.iliiw zgqep ly zlaewnd dwfgd dxevd `id zeey od dl` zeieyi izyy zxne`d dprhd dgkedd.ep`ady efn xzei zeyw zvw ze`xp olek la`,iliiw zgqepl zepey zegked ixqixz yi.chen ly `id dgexa xzeia dl daexwd