\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\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{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\citation{SS}
\citation{L}
\newlabel{ex:sigma}{{1.1}{2}{}{theorem.1.1}{}}
\newlabel{ex:k}{{1.2}{2}{}{theorem.1.2}{}}
\newlabel{thm:main}{{1.5}{2}{}{theorem.1.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}A collection of HTP sequences}{3}{section.2}}
\newlabel{sec:seq}{{2}{3}{A collection of HTP sequences}{section.2}{}}
\newlabel{rem:0}{{2.2}{3}{}{theorem.2.2}{}}
\newlabel{def:recurrence}{{2.3}{3}{}{theorem.2.3}{}}
\newlabel{def:U}{{2.4}{3}{}{theorem.2.4}{}}
\newlabel{def:seq}{{2.5}{4}{}{theorem.2.5}{}}
\newlabel{lem:T00}{{2.8}{5}{}{theorem.2.8}{}}
\newlabel{lem:leading}{{2.9}{6}{}{theorem.2.9}{}}
\newlabel{lem:x}{{2.10}{6}{}{theorem.2.10}{}}
\newlabel{lem:commute}{{2.11}{6}{}{theorem.2.11}{}}
\newlabel{lem:first}{{2.12}{7}{}{theorem.2.12}{}}
\newlabel{lem:2i+1}{{2.13}{7}{}{theorem.2.13}{}}
\newlabel{lem:Hankel}{{2.14}{7}{}{theorem.2.14}{}}
\newlabel{cor:preserve}{{2.15}{8}{}{theorem.2.15}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Classifying all $HTP$ sequences}{8}{section.3}}
\newlabel{sec:classify}{{3}{8}{Classifying all $HTP$ sequences}{section.3}{}}
\newlabel{lem:irreducible}{{3.1}{8}{}{theorem.3.1}{}}
\newlabel{lem:2n}{{3.2}{9}{}{theorem.3.2}{}}
\newlabel{lem:n=1}{{3.3}{9}{}{theorem.3.3}{}}
\newlabel{lem:divisible}{{3.4}{9}{}{theorem.3.4}{}}
\newlabel{lem:advance}{{3.5}{11}{}{theorem.3.5}{}}
\newlabel{thm:group}{{3.6}{12}{}{theorem.3.6}{}}
\newlabel{lem:inverse}{{3.7}{12}{}{theorem.3.7}{}}
\bibcite{CF}{1}
\bibcite{E}{2}
\bibcite{L}{3}
\bibcite{R}{4}
\bibcite{SS}{5}
\bibcite{W}{6}