\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\citation{gkp89}
\citation{cl96}
\citation{d97}
\citation{h69}
\@writefile{brf}{\backcite{gkp89}{{1}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{cl96,d97,h69}{{1}{(document)}{Doc-Start}}}
\newlabel{T:main}{{1.1}{1}{\relax }{fact.1.1}{}}
\citation{OEIS}
\newlabel{seq}{{1}{2}{\relax }{Item.1}{}}
\@writefile{brf}{\backcite{OEIS}{{2}{1}{Item.1}}}
\newlabel{eo}{{2}{2}{\relax }{Item.2}{}}
\newlabel{floor}{{3}{2}{\relax }{Item.3}{}}
\newlabel{fs}{{4}{2}{\relax }{Item.4}{}}
\newlabel{sum}{{5}{2}{\relax }{Item.5}{}}
\newlabel{sumflr}{{6}{2}{\relax }{Item.6}{}}
\newlabel{gf}{{7}{2}{\relax }{Item.7}{}}
\newlabel{rr}{{8}{2}{\relax }{Item.8}{}}
\newlabel{rra}{{8a}{2}{\relax }{Item.9}{}}
\newlabel{recp}{{8b}{2}{\relax }{Item.10}{}}
\newlabel{rec}{{8c}{2}{\relax }{Item.11}{}}
\newlabel{rrd}{{8d}{2}{\relax }{Item.12}{}}
\citation{OEIS}
\citation{s61cjm}
\newlabel{rre}{{8e}{3}{\relax }{Item.13}{}}
\newlabel{rrf}{{8f}{3}{\relax }{Item.14}{}}
\newlabel{delq}{{9}{3}{\relax }{Item.15}{}}
\newlabel{diff}{{9a}{3}{\relax }{Item.16}{}}
\@writefile{brf}{\backcite{OEIS}{{3}{9a}{Item.16}}}
\newlabel{d1}{{9b}{3}{\relax }{Item.17}{}}
\newlabel{dp}{{9c}{3}{\relax }{Item.18}{}}
\newlabel{delq3}{{9d}{3}{\relax }{Item.19}{}}
\newlabel{delq4}{{9e}{3}{\relax }{Item.20}{}}
\newlabel{d2}{{9f}{3}{\relax }{Item.21}{}}
\newlabel{de}{{10}{3}{\relax }{Item.22}{}}
\newlabel{dea}{{10a}{3}{\relax }{Item.23}{}}
\newlabel{deb}{{10b}{3}{\relax }{Item.24}{}}
\newlabel{dec}{{10c}{3}{\relax }{Item.25}{}}
\newlabel{ded}{{10d}{3}{\relax }{Item.26}{}}
\newlabel{dee}{{10e}{3}{\relax }{Item.27}{}}
\newlabel{quad}{{11}{3}{\relax }{Item.28}{}}
\citation{r78}
\citation{c94}
\citation{sw86}
\citation{f97}
\citation{s61cjm}
\citation{jm00amm}
\citation{m74amm}
\newlabel{spart}{{12}{4}{\relax }{Item.29}{}}
\newlabel{perm}{{13}{4}{\relax }{Item.30}{}}
\@writefile{brf}{\backcite{s61cjm}{{4}{13}{Item.30}}}
\newlabel{part}{{14}{4}{\relax }{Item.31}{}}
\@writefile{brf}{\backcite{r78}{{4}{14}{Item.31}}}
\newlabel{pp}{{15}{4}{\relax }{Item.32}{}}
\@writefile{brf}{\backcite{c94}{{4}{15}{Item.32}}}
\@writefile{brf}{\backcite{sw86}{{4}{15}{Item.32}}}
\@writefile{brf}{\backcite{f97}{{4}{15}{Item.32}}}
\@writefile{brf}{\backcite{s61cjm}{{4}{15}{Item.32}}}
\newlabel{gphc}{{16}{4}{\relax }{Item.33}{}}
\newlabel{gpha}{{17}{4}{\relax }{Item.34}{}}
\newlabel{gphd}{{18}{4}{\relax }{Item.35}{}}
\newlabel{gen}{{19}{4}{\relax }{Item.36}{}}
\newlabel{mgph}{{20}{4}{\relax }{Item.37}{}}
\newlabel{tri}{{22}{4}{\relax }{Item.39}{}}
\@writefile{brf}{\backcite{jm00amm,m74amm}{{4}{22}{Item.39}}}
\citation{class}
\citation{OEIS}
\newlabel{put}{{23}{5}{\relax }{Item.40}{}}
\newlabel{los}{{24}{5}{\relax }{Item.41}{}}
\@writefile{brf}{\backcite{class}{{5}{24}{Item.41}}}
\@writefile{brf}{\backcite{OEIS}{{5}{24}{Item.41}}}
\newlabel{cp}{{25}{5}{\relax }{Item.42}{}}
\newlabel{sa}{{26}{5}{\relax }{Item.43}{}}
\newlabel{i-pd}{{27}{5}{\relax }{Item.44}{}}
\citation{bkm95}
\citation{OEIS}
\citation{f55}
\citation{cse}
\citation{c00}
\citation{gkp89}
\citation{OEIS}
\citation{gsww92}
\citation{pw00}
\citation{ng56}
\citation{f68}
\citation{s00}
\newlabel{i-t}{{28}{6}{\relax }{Item.45}{}}
\newlabel{i-opt}{{29}{6}{\relax }{Item.46}{}}
\newlabel{last}{{29}{6}{\relax }{Item.46}{}}
\@writefile{brf}{\backcite{bkm95}{{6}{29}{Item.46}}}
\@writefile{brf}{\backcite{OEIS}{{6}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{f55}{{6}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{cse}{{6}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{c00}{{6}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{gkp89}{{6}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{OEIS}{{6}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{gsww92}{{6}{(document)}{Doc-Start}}}
\@writefile{brf}{\backcite{pw00}{{6}{(document)}{Doc-Start}}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Antagonistic functions}{6}{section.2}}
\newlabel{s-antf}{{2}{6}{Antagonistic functions\relax }{section.2}{}}
\@writefile{brf}{\backcite{ng56}{{6}{2}{Item.49}}}
\@writefile{brf}{\backcite{f68}{{6}{2}{Item.49}}}
\@writefile{brf}{\backcite{s00}{{6}{2}{Item.49}}}
\citation{gkp89}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Examples which are not antagonistic}{7}{subsection.2.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Properties of antagonistic functions}{7}{subsection.2.2}}
\newlabel{l-antg1}{{2.2}{7}{Properties of antagonistic functions\relax }{fact.2.2}{}}
\newlabel{l:antg2}{{2.3}{7}{Properties of antagonistic functions\relax }{fact.2.3}{}}
\@writefile{brf}{\backcite{gkp89}{{7}{2.2}{fact.2.3}}}
\newlabel{f-fun}{{2.4}{7}{Properties of antagonistic functions\relax }{fact.2.4}{}}
\citation{cm89dm}
\citation{cmm00dm}
\newlabel{antg}{{2.6}{8}{Properties of antagonistic functions\relax }{fact.2.6}{}}
\newlabel{f-fn}{{2.7}{8}{Properties of antagonistic functions\relax }{fact.2.7}{}}
\@writefile{brf}{\backcite{cm89dm}{{8}{2.2}{fact.2.7}}}
\@writefile{brf}{\backcite{cmm00dm}{{8}{2.2}{fact.2.7}}}
\citation{gkp89}
\@writefile{toc}{\contentsline {section}{\numberline {3}Proof of the theorem}{9}{section.3}}
\@writefile{brf}{\backcite{gkp89}{{9}{3}{section.3}}}
\citation{m90}
\@writefile{brf}{\backcite{m90}{{10}{3}{section.3}}}
\citation{m90}
\citation{c94}
\citation{sw86}
\@writefile{brf}{\backcite{m90}{{11}{3}{section.3}}}
\@writefile{brf}{\backcite{c94}{{11}{3}{section.3}}}
\@writefile{brf}{\backcite{sw86}{{11}{3}{section.3}}}
\citation{ng56}
\citation{cl96}
\citation{b73}
\@writefile{brf}{\backcite{ng56}{{13}{3}{pseudocode.2}}}
\@writefile{brf}{\backcite{cl96}{{13}{3}{pseudocode.2}}}
\@writefile{brf}{\backcite{b73}{{13}{3}{pseudocode.2}}}
\citation{jm00amm}
\citation{a85}
\citation{r78}
\citation{a95amm}
\citation{ms65cjm}
\citation{b78}
\citation{b86}
\citation{b78}
\citation{ggl95v2}
\citation{h69}
\@writefile{brf}{\backcite{jm00amm}{{14}{3}{pseudocode.2}}}
\@writefile{brf}{\backcite{a85}{{14}{3}{pseudocode.2}}}
\@writefile{brf}{\backcite{r78}{{14}{3}{pseudocode.2}}}
\@writefile{brf}{\backcite{a95amm,ms65cjm}{{14}{3.1}{fact.3.1}}}
\@writefile{brf}{\backcite{b78}{{14}{1}{Item.52}}}
\@writefile{brf}{\backcite{b86}{{14}{1}{Item.52}}}
\@writefile{brf}{\backcite{b78}{{14}{2}{Item.53}}}
\@writefile{brf}{\backcite{ggl95v2}{{14}{2}{Item.53}}}
\@writefile{brf}{\backcite{h69}{{14}{3}{Item.54}}}
\citation{bkm95}
\citation{EIS}
\citation{a94}
\citation{p56}
\citation{r78}
\bibcite{a95amm}{1}
\bibcite{a85}{2}
\@writefile{brf}{\backcite{bkm95}{{15}{3}{Item.55}}}
\@writefile{brf}{\backcite{EIS}{{15}{3}{Item.55}}}
\@writefile{brf}{\backcite{a94}{{15}{3.2}{fact.3.2}}}
\@writefile{brf}{\backcite{p56}{{15}{3.2}{fact.3.2}}}
\@writefile{brf}{\backcite{r78}{{15}{3.2}{fact.3.2}}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Acknowledgements}{15}{section.4}}
\bibcite{a94}{3}
\bibcite{bkm95}{4}
\bibcite{b73}{5}
\bibcite{b78}{6}
\bibcite{b86}{7}
\bibcite{c94}{8}
\bibcite{c00}{9}
\bibcite{cl96}{10}
\bibcite{cmm00dm}{11}
\bibcite{cm89dm}{12}
\bibcite{d97}{13}
\bibcite{cse}{14}
\bibcite{f68}{15}
\bibcite{f55}{16}
\bibcite{f97}{17}
\bibcite{gsww92}{18}
\bibcite{ggl95v2}{19}
\bibcite{gkp89}{20}
\bibcite{h69}{21}
\bibcite{jm00amm}{22}
\bibcite{m74amm}{23}
\bibcite{m90}{24}
\bibcite{ms65cjm}{25}
\bibcite{ng56}{26}
\bibcite{pw00}{27}
\bibcite{p56}{28}
\bibcite{r78}{29}
\bibcite{s61cjm}{30}
\bibcite{OEIS}{31}
\bibcite{class}{32}
\bibcite{EIS}{33}
\bibcite{s00}{34}
\bibcite{sw86}{35}