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Ranking of k-permutations.
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1 % TeX macros for typesetting my PhD thesis
2 % (c) 2008 Martin Mares <mj@ucw.cz>
3
4 \input epsf.tex
5 \input btxmac.tex
6 %\input amssym.tex
7
8 \catcode`@=11
9
10 %%% Basic parameters %%%
11
12 % A4 with 1in margins, leaving 20pt for page numbering at the bottom
13 \hsize=159mm
14 \vsize=246mm
15 \advance\vsize by -20pt
16 \parindent=0.8cm
17 \parskip=3pt plus 1pt minus 1pt
18
19 \smallskipamount=4pt plus 1.2pt minus 1.2pt
20 \medskipamount=7pt plus 2.5pt minus 2pt
21 \bigskipamount=15pt plus 5pt minus 4pt
22
23 \abovedisplayskip=15pt plus 4pt minus 10pt
24 \abovedisplayshortskip=0pt plus 3pt
25 \belowdisplayskip=15pt plus 4pt minus 10pt
26 \belowdisplayshortskip=8.5pt plus 3.5pt minus 4.5pt
27
28 %%% Miscellanea %%%
29
30 \def\em#1{{\it #1\/}}
31 \def\df#1{{\it #1\/}}   % when we define something
32 \def\O{{\cal O}}
33 \def\<#1>{\leavevmode\hbox{\it #1\/}}
34 \let\>=\noindent
35 \def\qed{{\parfillskip=0pt\allowbreak\hfill\nobreak $\spadesuit$\par}}
36 \def\qeditem{{\parfillskip=0pt\hfill\rlap{\hskip\rightskip\llap{$\spadesuit$}}\par}}
37 \def\FIXME#1{\>{\bo TODO:} #1}
38 \def\symdiff{\mathbin{\Delta}}
39 \def\rack#1#2{\setbox0=\hbox{#1}\hbox to \wd0{#2}}
40 \def\o#1{\accent23 #1}
41 \def\mst{\mathop{\rm mst}}
42 \def\deg{\mathop{\rm deg}}
43 \def\timesalpha{\mskip2mu\alpha}
44 \def\timesbeta{\mskip2mu\beta}
45 \def\tower{\mathop\uparrow}
46
47 % Bit strings
48 \def\0{{\bf 0}}
49 \def\1{{\bf 1}}
50 \def\(#1){\mathord{\left<#1\right>}}
51
52 % Bitwise operations
53 \def\shl{\mathbin{<\!<}}
54 \def\shr{\mathbin{>\!>}}
55 \def\bop#1{\mathbin{\hbox{\sc #1}}}
56 \def\band{\bop{and}}
57 \def\bor{\bop{or}}
58 \def\bxor{\bop{xor}}
59 \def\bnot{\mathop{\hbox{\sc not}}}
60
61 % A reversed version of \ddots with extra space at the top to get good alignment of exponents.
62 \def\rddots{\mathinner{\mkern1mu\raise\p@\vbox{\kern7\p@\hbox{.}}\mkern2mu
63     \raise4\p@\hbox{.}\mkern2mu\raise7\p@\hbox{.}\raise11\p@\hbox{}\mkern1mu}}
64
65 % Footnotes
66 \newcount\footcnt
67 \footcnt=0
68 \def\foot#1{\global\advance\footcnt by 1{\parindent=0.25in\parskip=0pt\footnote{$^{\bf\the\footcnt}$}{#1}}}
69
70 %%% Fonts %%%
71
72 \font\twelverm=cmr12
73 \font\twelveit=cmti12
74 \font\twelvebf=cmbx12
75
76 %\font\twelverm=pplr8z at 12pt
77 %\font\twelveit=pplri8z at 12pt
78 %\font\twelvebf=pplb8z at 12pt
79
80 \font\twelvesl=cmsl12
81 \font\twelveb=cmb12
82 \font\twelvesc=cmcsc12
83
84 \def\mathf@nt#1#2#3#4{%
85 \toks0=\expandafter{\csname#1#2\endcsname}%
86 \expandafter\ifx\the\toks0\relax%
87 %\immediate\write-1{bb \the\toks0=#4#2#3}%
88 \global\expandafter\font\the\toks0=#4#2#3%
89 \fi%
90 \edef\m@@f{\the\toks0}}
91
92 \def\fntmathsize{12}
93 \def\fntmathtok{twelve}
94 \def\fntmathssize{8}
95 \def\fntmathstok{eight}
96 \def\fntmathsssize{6}
97 \def\fntmathsstok{six}
98
99 \mathf@nt{\fntmathtok}{r}{\fntmathsize}{cm}\textfont0=\m@@f
100 \mathf@nt{\fntmathstok}{r}{\fntmathssize}{cm}\scriptfont0=\m@@f
101 \mathf@nt{\fntmathsstok}{r}{\fntmathsssize}{cm}\scriptscriptfont0=\m@@f
102 \mathf@nt{\fntmathtok}{mi}{\fntmathsize}{cm}\skewchar\m@@f='177\textfont1=\m@@f
103 \mathf@nt{\fntmathstok}{mi}{\fntmathssize}{cm}\skewchar\m@@f='177\scriptfont1=\m@@f
104 \mathf@nt{\fntmathsstok}{mi}{\fntmathsssize}{cm}\skewchar\m@@f='177\scriptscriptfont1=\m@@f
105 \mathf@nt{\fntmathtok}{sy}{\fntmathsize}{cm}\skewchar\m@@f='60\textfont2=\m@@f
106 \mathf@nt{\fntmathstok}{sy}{\fntmathssize}{cm}\skewchar\m@@f='60\scriptfont2=\m@@f
107 \mathf@nt{\fntmathsstok}{sy}{\fntmathsssize}{cm}\skewchar\m@@f='60\scriptscriptfont2=\m@@f
108 \mathf@nt{\fntmathtok}{ex}{\fntmathsize}{cm}\textfont3=\m@@f\scriptfont3=\m@@f\scriptscriptfont3=\m@@f
109 \mathf@nt{\fntmathtok}{ti}{\fntmathsize}{cm}\textfont\itfam=\m@@f
110 \mathf@nt{\fntmathtok}{sl}{\fntmathsize}{cm}\textfont\slfam=\m@@f
111 \mathf@nt{\fntmathtok}{bx}{\fntmathsize}{cm}\textfont\bffam=\m@@f
112 \mathf@nt{\fntmathtok}{tt}{\fntmathsize}{cm}\hyphenchar\m@@f=-1\textfont\ttfam=\m@@f
113 %\mathf@nt{\fntmathtok}{msam}{\fntmathsize}{}\textfont\msafam=\m@@f
114 %\mathf@nt{\fntmathstok}{msam}{\fntmathssize}{}\scriptfont\msafam=\m@@f
115 %\mathf@nt{\fntmathsstok}{msam}{\fntmathsssize}{}\scriptscriptfont\msafam=\m@@f
116 %\mathf@nt{\fntmathtok}{msbm}{\fntmathsize}{}\textfont\msbfam=\m@@f
117 %\mathf@nt{\fntmathstok}{msbm}{\fntmathssize}{}\scriptfont\msbfam=\m@@f
118 %\mathf@nt{\fntmathsstok}{msbm}{\fntmathsssize}{}\scriptscriptfont\msbfam=\m@@f
119
120 % Blackboard bold font
121 \newfam\bbfam
122 \font\bbtwelve=bbm12
123 \font\bbeight=bbm8
124 \font\bbsix=bbm6
125 \textfont\bbfam=\bbtwelve
126 \scriptfont\bbfam=\bbeight
127 \scriptscriptfont\bbfam=\bbsix
128 \def\bb{\bbtwelve\fam\bbfam}
129
130 % Font switches
131 \def\rm{\fam\z@\twelverm}
132 \def\it{\fam\itfam\twelveit}
133 \def\bo{\fam\bffam\twelveb}
134 \def\bf{\fam\bffam\twelvebf}
135 \def\tt{\fam\ttfam\twelvett\hyphenchar\twelvett=-1\relax}
136 \def\sc{\twelvesc}
137 \def\sl{\fam\slfam\twelvesl}
138
139 % Switch to 12pt baselines
140 \rm
141 \baselineskip=14.4pt
142 \lineskip=1.2pt
143 \setbox\strutbox=\hbox{\vrule height 10.2pt depth 4.2pt width 0pt}
144
145 % Other fonts
146 \font\chapfont=csssdc17 scaled \magstep1
147 \font\secfont=csb14
148 \font\secitfont=csbxti14
149
150 %%% FIXME
151 \footline={\hss\twelverm\folio\hss}
152
153 %%% Enumerated lists %%%
154
155 \newif\ifitem\itemtrue
156 \newbox\itembox
157 \newcount\itemcount
158
159 \def\interlistskip{\vskip 3pt plus 2pt minus 1pt}
160
161 \def\itemspacingrules{\ifitem\advance\leftskip by \parindent\parindent=0pt\itemfalse\else
162 \advance\leftskip by 2.5em\fi\rightskip=\leftskip}
163
164 \def\inititemize{\interlistskip\begingroup
165 \parskip=1pt plus 0.3pt minus 0.1pt
166 \itemspacingrules}
167
168 \def\itemize#1{\inititemize\setbox\itembox\llap{#1\hskip 0.4em}%
169 \let\:=\singleitem}
170
171 \def\singleitem{\par\leavevmode\copy\itembox}
172
173 \def\endlist{\interlistskip\endgroup}
174
175 \def\ibull{\raise0.2ex\hbox{$\bullet$}} % Signs frequently used for \itemize
176 \def\idot{\raise0.2ex\hbox{$\cdot$}}
177 \def\istar{\raise0.2ex\hbox{$\ast$}}
178
179 \def\numlist#1{\inititemize\itemcount=0\let\:=\numbereditem
180 \let\itemnumbering=#1}
181
182 \def\numbereditem{\par\leavevmode\advance\itemcount by 1
183 \llap{\itemnumbering\hskip 0.4em}}
184
185 \def\nnorm{\the\itemcount}
186 \def\ndotted{\nnorm.}
187 \def\nparen{\nnorm)}
188 \def\nroman{\romannumeral\itemcount}
189 \def\nromanp{\nroman)}
190 \def\nalpha{\count@=96\advance\count@ by\itemcount\char\count@)}
191 \def\nAlpha{\count@=64\advance\count@ by\itemcount\char\count@)}
192 \def\ngreek{$\ifcase\itemcount\or\alpha\or\beta\or\gamma\or\delta\or\epsilon\or
193 \zeta\or\eta\or\theta\or\iota\or\kappa\or\lambda\or\mu\or\nu\or\xi\or\pi\or\rho
194 \or\sigma\or\tau\or\upsilon\or\phi\or\chi\or\psi\or\omega\fi$)}
195
196 % New \frenchspacing, which doesn't leave unwanted spaces in text.
197 \def\frenchsp@cing{\sfcode`\.\@m \sfcode`\?\@m \sfcode`\!\@m%
198 \sfcode`\:\@m \sfcode`\;\@m \sfcode`\,\@m}
199
200 %%% Local verbatim mode %%%
201
202 \def\make@ther#1{\catcode`#1=12\relax}
203 \def\setverb@tim{\tt\frenchsp@cing\catcode`\`=13\catcode`\'=13\n@ligs%
204 \let\do=\make@ther\dospecials\obeyspaces}
205
206 {\catcode`'=13
207 \catcode``=13
208 \gdef\n@ligs{\def`{\relax\lq}\def'{\relax\rq}}}
209
210 {\obeyspaces
211 \global\chardef\sp@ce=32
212 \gdef\showspaces{\let =\sp@ce}
213 \global\let =\ }
214
215 \catcode124=\active % Make | active
216 \def\ttst@rt{\begingroup\setverb@tim\let|=\endgroup}
217 \let|=\ttst@rt
218
219 %%% Verbatim mode for text in { } %%%
220
221 \newskip\verbglue\newskip\verblineglue
222 \verbglue=3pt plus 1pt minus 0.3pt
223 \verblineglue=0pt plus 1.5pt
224 \def\verblocaldefs{}
225
226 \newdimen\tabwidth
227 \newcount\tabsize
228 \tabsize=8
229 \newdimen\t@b
230
231 \newcount\vercnt
232 \def\v@rbend{\par\endgroup\vskip\verbglue}
233 \def\v@rbl{\ifnum\vercnt>0\{\fi\global\advance\vercnt by 1\relax}
234 \def\v@rbr{\ifnum\vercnt>1\}\else\v@rbend\fi\global\advance\vercnt by -1\relax}
235 \def\v@rbparams{\setverb@tim\parskip=\verblineglue\parindent=0pt\raggedbottom%
236 \rightskip\z@ plus1fil\pretolerance=10000\tolerance=10000\vercnt=0%
237 \catcode124=12\setupt@bs\vskip\verbglue\defb@x\obeylines}
238
239 \def\startb@x{\setbox0=\hbox\bgroup}
240 \def\defb@x{\def\par{\leavevmode\egroup\box0\endgraf}%
241 \everypar{\startb@x}}
242
243 {\catcode`\^^I=\active
244 \gdef\setupt@bs{\catcode`\^^I=\active
245 \setbox0=\hbox{\tt\ }\tabwidth=\wd0\multiply\tabwidth by \tabsize
246 \def^^I{\leavevmode\egroup\t@b=\wd0\divide\t@b by \tabwidth%
247 \multiply\t@b by \tabwidth%
248 \advance\t@b by \tabwidth\advance\t@b by -\wd0\box0\hbox to \t@b{}\startb@x}
249 }}
250
251 {
252 \catcode`[=1\catcode`]=2\catcode123=\active\catcode125=\active
253 \gdef\verbatim[\begingroup\v@rbparams\catcode123=\active\catcode125=\active%
254 \let{=\v@rbl\let}=\v@rbr\chardef\{=123\chardef\}=125\verblocaldefs
255 ]]
256
257 \def\verbinput#1{\begingroup\v@rbparams\input #1\endgroup}
258
259 %%% Algorithms %%%
260
261 %       \algo{jmeno algoritmu}
262 %       \algin popis vstupu
263 %       \:krok
264 %       \:krok
265 %       \::vnoreny krok
266 %       \algout popis vystupu
267 %       \endalgo
268
269 \def\algo{
270 \interlistskip
271 \begingroup
272 \let\:=\algoitem
273 \parskip=1pt plus 1pt minus 0.3pt
274 \rightskip=2em
275 \itemcount=0
276 \smallskip
277 }
278 \def\endalgo{\interlistskip\endgroup}
279 \def\algopar{\par
280 \parindent=2em
281 \hangindent=4em
282 \hangafter=1
283 \leavevmode
284 }
285 \def\algoitem{
286 \algopar\advance\itemcount by 1
287 \hbox to 2em{\hss \the\itemcount. }%
288 \futurelet\next\algoitemh}
289 \def\algoitemh{\ifx\next:\let\next=\algohang\else\let\next=\relax\fi\next}
290 \def\algohang:{\advance\hangindent by 2em \hskip 2em\futurelet\next\algoitemh}
291 \def\algin{\par{\sl Input:\/} }
292 \def\algout{\par{\sl Output:\/} }
293
294 %%% Constructs used in algorithms %%%
295
296 \def\={\leftarrow}
297 \def\cmt#1{~~{\sl (#1)}}
298
299 %%% Chapters, sections and proclamations %%%
300
301 \newcount\chapcount
302 \newcount\seccount
303 \newcount\thmcount
304 \chapcount=0
305 \seccount=0
306 \thmcount=0
307 \def\currentid{??}
308
309 \def\chapter#1{\vfill\supereject
310 \advance\chapcount by 1
311 \seccount=0
312 \thmcount=0
313 \footcnt=0
314 \edef\currentid{\the\chapcount}
315 \leftline{\chapfont\currentid. #1}
316 \bigskip
317 }
318
319 \def\section#1{\bigskip
320 \advance\seccount by 1
321 \thmcount=0
322 \edef\currentid{\the\chapcount.\the\seccount}
323 \leftline{\secfont\currentid. #1}
324 \medskip
325 }
326
327 \def\para{\advance\thmcount by 1
328 \edef\currentid{\the\chapcount.\the\seccount.\the\thmcount}
329 \noindent {\bo \currentid.\enspace}}
330
331 \def\proclaim#1{\para {\bo #1.\enspace}}
332
333 \def\thm{\proclaim{Theorem}}
334 \def\lemma{\proclaim{Lemma}}
335 \def\defn{\proclaim{Definition}}
336 \def\problem{\proclaim{Problem}}
337 \def\obs{\proclaim{Observation}}
338 \def\rem{\proclaim{Remark}}
339 \def\alg{\proclaim{Algorithm}}
340 \def\impl{\proclaim{Implementation}}
341 \def\cor{\proclaim{Corollary}}
342 \def\nota{\proclaim{Notation}}
343 \def\example{\proclaim{Example}}
344
345 \def\label#1{{\sl (#1)\/}\enspace}
346
347 \def\thmn{\thm\label}
348 \def\lemman{\lemma\label}
349 \def\defnn{\defn\label}
350 \def\algn{\alg\label}
351 \def\notan{\nota\label}
352
353 \def\proof{\noindent {\sl Proof.}\enspace}
354 \def\proofsketch{\noindent {\sl Proof sketch.}\enspace}
355
356 %%% References %%%
357
358 \newwrite\ids
359 \def\writeid#1#2{\immediate\write\ids{\string\def\expandafter\string\csname id#1\endcsname{#2}}}
360
361 \immediate\openin\ids=\jobname.ids
362 \ifeof\ids
363 \else
364 \input \jobname.ids
365 \fi
366 \immediate\closein\ids
367 \immediate\openout\ids=\jobname.ids
368
369 \def\ref#1{\expandafter\ifx\csname id#1\endcsname\relax
370 {\bo ??}%
371 \immediate\write16{*** Warning: Reference #1 undefined ***}%
372 \else
373 \csname id#1\endcsname
374 \fi
375 }
376
377 \def\id#1{\writeid{#1}{\currentid}}
378
379 %%% Bibliography %%%
380
381 %\bibliographystyle{abbrv}
382 \bibliographystyle{alpha}
383 \def\dumpbib{
384   \def\bblhook{\parskip=2pt plus 1pt minus 0.5pt}
385   \bibliography{biblio}
386 }
387
388 %%% Figures %%%
389
390 \def\figure#1#2#3{\midinsert
391 \medskip
392 \centerline{\epsfxsize=#2\epsfbox{pic/#1}}
393 \medskip
394 \smallskip
395 \centerline{#3}
396 \endinsert}
397
398 %%% Stand-alone chapters %%%
399
400 \def\endpart{
401   \section{Bibliography}
402   \dumpbib
403   \vfill\supereject\end
404 }
405
406 %%% The End %%%
407
408 \catcode`@=12