%% 428 \input style \subsubchap{䈑 } , . . " " " " , : \medskip \item{i)} 䋟 . \item{ii)} ዎ, , () . \medskip \noindent 쀃 (ii), (i), . 텊 (i), (ii); , \picture{. 89.  } . ꀆ , , ; , - .  . .  , (i) (ii), %% 429 (. 89). 䀍 , ; . " /" . ꀆ , \emph{} \emph{}, / . 䅐 --- , / , . 썎 , , \emph{}. 퀏, .~89 , / ; , , . , |MIXTEC|, $$ \eqalign{ \hbox{1 }& =\hbox{5000 ,}\cr \hbox{1 }& =\hbox{20 ,}\cr \hbox{1 }&= \hbox{200 .}\cr } $$ 򀊎 20 , . . , . , . , |MIXTEC|, , . ␅, , , , : \itemize \li ␅ (, ). \li ␅ (, , / ). \li ␅ (, , ). \itemend |MIXTEC| $i$ $j$ $25+{1\over2}\vert i-j \vert$ . 呋 $i$ $j$--- 1 200, %%430 $\vert i-j\vert$ $2 \left( {201\atop 3}\right)/200^2\approx 66.7$, . . 60~. 䈑 |MIXTEC| 25 , 12.5 . ␅ $n$ $(n/5000)\times25\hbox{ }=5n\hbox{ }$. ( $3{1\over3}$ , |MIXT|, .~5.4.6.) 򀊈 , |MIXTEC| |MIXT|, , : \medskip \item{a)} . \item{b)}  , , ( + ). \item{c)} 񊎐 . \medskip 葏 , (a). 򅏅 --- , (b). \qsection ꀊ ? . , , , /, . 텋 , - , . 텑, , . ⎒ "" . \enumerate \li 呋 , ( ) , . ⎎ , / - . \li (.~90): , $A$, , , .. ${1\over2}\times25$ . 呋 , $B$, ${1\over 4}$ $1\over2$ ; %%431 ${3\over4}\times25$ . 퀈 , $C$: , \emph{} $3\over4$ . 쎆 , ${1\over2}\times25$ . , . , $C$.  \picture{. 90. } , , + . 񐅄 ${1\over2}(1-x^2)$ , $x$ ($0 , . .~5.4.4, , , . ("$T$-lifo" " $T$-fifo"), "" . \emph{ }, (. . ). 񋅄, , , , $P$- , $P$--- , . (5.4.4--9) %% 434 $S$ () $$ qS-\lfloor(P^q-S)/(P-1)\rfloor, \qquad q=\lceil\log_P S\rceil. \eqno(1) $$  , $P$- . (., , .~91, $P=3$, $S=6$.) 񍀗 , , " ", $S\equiv1 \pmod{P-1}$; " --- \picture{. 92.  ...} ", $P$ "" , .  $P$- , , , .  (. 2.3.4.5--10), : " $(1-S)\bmod(P-1)$ 0, $P$ \emph{} , ". 呋 , . 100000, 9- , 18 , 5.4.6F .  9- 60 $1{29\over30}$ , . .  " " , , 7.4 . 󂅋 $P$, , , , . %%435 \section ⋈ .  , "" , . , , .  . 󌅍 $P$ . , ; , $P$. ␅ , , , . ᛒ , .  . (., , .~2). ꐎ , , - ; , , ! 򀊈 , , "" , . 퀘 , (. . ), ; , . , , .~92; , ' , . , . , (1) $n$ $72.5+0.005n$~; (2) 100000 ; (3) $0.004$~ ; (4) \emph{ } , ; (5) , , , . . 呋 $P$- , %% 436 $P+1$ : $P$--- 1--- ; $B=100000/(P+1)$ . , $L$ ; $L/B$ ; , ( ) $$ 2\left(72.5{L\over B}+0.005L\right)+0.004L=(0.00145P+0.011545)L. \eqno(2) $$ 荛 , $P$- $L$ $(\alpha P+\beta)L$ , $\alpha$ ~$\beta$--- , , , . \picture{. 92. 䅐 16 ...} . , , .~92 , . ( "") $L_0$.. 򎃄 9 ~10 $(2\alpha+\beta)(2L_0)$ , 11 $(3\alpha+\beta)(4L_0)$ 12 $(4\alpha+\beta)(8L_0)$ .  , , $(52\alpha + 16\beta)L_0$ . ꎝ "16" : . ꎝ "52" $\alpha$ , \dfn{ }; , , , . 퀏, .~92 $(2+4)+(2+4)+(3+4)+(2+3+4)+(2+3+4)+(3+4)+(4)+(4)=52$. 呋 $\cJ$--- , $D(\cJ)$, $E(\cJ)$ . : %% 437 \proclaim 򅎐 H. 呋 , $P$- $L$ , $(\alpha P+\beta)L$ $S$ , $\cJ$, $\alpha D (\cJ)+\beta E(\cJ)$ $S$ . \noindent ( , 䆎 . ACM 1963 .)  $\alpha$ $\beta$--- ; , \dfn{}, $\alpha D(\cJ)+\beta E (\cJ)$ $\cJ$ . 텒 , \emph{ }.  $n$ , , $n$ . \proclaim 򅎐 K.  $A_m(n)$ $1\le m\le n$ $$ \eqalignno{ A_1(1)&=0; & (3) \cr A_m(n)&=\min_{1\le k\le n/m} (A_1(k)+A_{m-1}(n-k) \rem{ $2\le m\le n$;} & (4) \cr A_1(n)&=\min_{2\le m\le n} ((\alpha mn+\beta n+A_m(n)) \rem{ $n\ge 2$.} & (5)\cr } $$ 򎃄 $A_1(n)$ $\alpha D (\cJ) +\beta E(\cJ)$ $\cJ$ $n$ . \proof (4) , $A_m(n)$ $A_1(n_1)+\cdots+A_1(n_m)$ $n_1$, \dots, $n_m$, , $n_1+\cdots+n_m=n$. 򐅁 ~$n$. \proofend (3), (4), (5) .  $k_m(n)$---, $A_m()$. 򎃄 $n$ , $m=k_1(n)$ ; $k_m(n)$, $k_{m-1}(n-k_m(n))$, $k_{m-2}(n-k_m(n)-k_{m-1}(n-k_m(n)))$, \dots . $\alpha=\beta=1$ .~1. ꎌ ; "4:9:9" $n=22$, , , $\cJ_22$ 22 $\cJ_4$, $\cJ_9$ ~$\cJ_9$ (.~93).  ; , 5:8:9 , 4:9:9. %% 438 \bye