\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]{}
\citation{Sl}
\citation{St2}
\citation{St3}
\citation{AignerMotzkin}
\citation{DONAGHEY}
\citation{EliMan}
\citation{ManSha}
\HyPL@Entry{0<</S/D>>}
\citation{FUR}
\citation{GarsiaHaiman}
\citation{HG}
\citation{ADIN}
\citation{flaj}
\citation{Oste}
\citation{BARCUCCI}
\citation{flaj}
\citation{ED}
\citation{flaj}
\citation{BARCUCCI}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
\citation{CHEN}
\@writefile{toc}{\contentsline {section}{\numberline {2}Motzkin tunnel polynomials}{3}{section.2}}
\newlabel{sectone}{{2}{3}{Motzkin tunnel polynomials}{section.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Basic definitions}{3}{subsection.2.1}}
\newlabel{esempio1}{{1}{4}{}{theorem.1}{}}
\citation{D2}
\citation{Sl}
\citation{Sl}
\newlabel{simmetria}{{4}{6}{}{theorem.4}{}}
\newlabel{fond}{{1}{6}{}{equation.2.1}{}}
\citation{Sl}
\citation{Sl}
\citation{Sl}
\citation{Sl}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Specializations}{7}{subsection.2.2}}
\newlabel{specmot}{{2.2}{7}{Specializations}{subsection.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}A joint distribution}{8}{subsection.2.3}}
\newlabel{jointd}{{2.3}{8}{A joint distribution}{subsection.2.3}{}}
\citation{KraLattice}
\citation{KraDet}
\citation{KraDetCom}
\citation{KraDetCom}
\@writefile{toc}{\contentsline {section}{\numberline {3}Catalan tunnel polynomials}{9}{section.3}}
\newlabel{catalan}{{3}{9}{Catalan tunnel polynomials}{section.3}{}}
\newlabel{simm}{{2}{10}{Catalan tunnel polynomials}{equation.3.2}{}}
\newlabel{ricorrcat}{{3}{10}{Catalan tunnel polynomials}{equation.3.3}{}}
\citation{Sl}
\citation{Sl}
\citation{Sl}
\citation{Fl}
\citation{Sl}
\citation{ACMS}
\citation{Sl}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Catalan specializations}{11}{subsection.3.1}}
\citation{FUR}
\citation{ADIN}
\citation{ADIN}
\citation{Ramanujan3}
\citation{Kn1}
\citation{Kn1}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}A joint Catalan distribution}{13}{subsection.3.2}}
\newlabel{Rama}{{4}{13}{A joint Catalan distribution}{equation.3.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Binary trees}{13}{section.4}}
\newlabel{fbt}{{4}{13}{Binary trees}{section.4}{}}
\citation{Kn1}
\citation{Sl}
\citation{Kn1}
\citation{CHEN}
\citation{Shapiro}
\citation{CHEN}
\citation{CHEN}
\@writefile{toc}{\contentsline {section}{\numberline {5}Partial and free Motzkin paths}{16}{section.5}}
\newlabel{Partialfree}{{5}{16}{Partial and free Motzkin paths}{section.5}{}}
\newlabel{bijectionpartialfree}{{12}{16}{}{theorem.12}{}}
\citation{CHEN}
\citation{CHEN}
\citation{CHEN}
\citation{Shapiro}
\newlabel{matrixeq}{{5}{18}{}{equation.5.5}{}}
\newlabel{equazionericorrenza}{{6}{18}{Partial and free Motzkin paths}{equation.5.6}{}}
\citation{ShapGetu}
\newlabel{generpartial}{{8}{19}{Partial and free Motzkin paths}{equation.5.8}{}}
\citation{Sl}
\newlabel{mat}{{9}{20}{Partial and free Motzkin paths}{equation.5.9}{}}
\newlabel{mat2}{{10}{20}{Partial and free Motzkin paths}{equation.5.10}{}}
\newlabel{recurrence2}{{11}{20}{Partial and free Motzkin paths}{equation.5.11}{}}
\citation{KraArchive}
\bibstyle{dersh-jis}
\bibdata{barnabei5}
\bibcite{ADIN}{1}
\bibcite{AignerMotzkin}{2}
\bibcite{ACMS}{3}
\bibcite{BARCUCCI}{4}
\bibcite{Ramanujan3}{5}
\bibcite{CHEN}{6}
\bibcite{D2}{7}
\bibcite{DONAGHEY}{8}
\bibcite{ED}{9}
\bibcite{EliMan}{10}
\bibcite{flaj}{11}
\@writefile{toc}{\contentsline {section}{\numberline {6}Acknowledgments}{21}{section.6}}
\bibcite{Fl}{12}
\bibcite{FUR}{13}
\bibcite{GarsiaHaiman}{14}
\bibcite{HG}{15}
\bibcite{Kn1}{16}
\bibcite{KraDet}{17}
\bibcite{KraDetCom}{18}
\bibcite{KraLattice}{19}
\bibcite{KraArchive}{20}
\bibcite{ManSha}{21}
\bibcite{Oste}{22}
\bibcite{ShapGetu}{23}
\bibcite{Shapiro}{24}
\bibcite{Sl}{25}
\bibcite{St2}{26}
\bibcite{St3}{27}
