\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{AcetoMalonekTomaz2017}
\citation{CacaoFalcaoMalonek2012}
\citation{CacaoFalcaoMalonek2017}
\citation{FalcaoCruzMalonek2006}
\citation{FalcaoMalonek2007}
\citation{MalonekFalcao2007}
\citation{BockGurlebeck2010}
\citation{CacaoMalonek2008}
\citation{CacaoFalcaoMalonek2011}
\citation{CacaoMalonek2011a}
\citation{CruzFalcaoMalonek2011}
\citation{Eelbode2012}
\citation{Guerlebeck2009}
\citation{Lavicka2010}
\citation{Lavicka2012}
\citation{MoraisLe2011}
\HyPL@Entry{0<</S/D>>}
\citation{CacaoFalcaoMalonek2017a}
\citation{CruzFalcaoMalonek2014}
\citation{FalcaoMalonek2012b}
\citation{MalonekFalcao2011}
\@writefile{toc}{\contentsline {section}{\numberline {1}Motivation}{2}{section.1}}
\newlabel{sec:1}{{1}{2}{Motivation}{section.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}A multidimensional polynomial sequence}{2}{section.2}}
\newlabel{sec:2}{{2}{2}{A multidimensional polynomial sequence}{section.2}{}}
\citation{GuerlebeckMalonek1999}
\citation{Malonek2004}
\citation{FalcaoMalonek2007}
\citation{MalonekFalcao2007}
\citation{FalcaoMalonek2007}
\citation{FalcaoMalonek2012b}
\citation{MalonekFalcao2010}
\newlabel{pkn:1}{{1}{3}{A multidimensional polynomial sequence}{equation.2.1}{}}
\newlabel{tks:1}{{2}{3}{A multidimensional polynomial sequence}{equation.2.2}{}}
\citation{FalcaoMalonek2012b}
\citation{OEIS}
\citation{CacaoFalcaoMalonek2017a}
\citation{CacaoFalcaoMalonek2017a}
\citation{CacaoFalcaoMalonek2017a}
\newlabel{pkn:2}{{3}{4}{A multidimensional polynomial sequence}{equation.2.3}{}}
\newlabel{ck}{{4}{4}{A multidimensional polynomial sequence}{equation.2.4}{}}
\newlabel{alternating sum}{{5}{4}{A multidimensional polynomial sequence}{equation.2.5}{}}
\newlabel{partition}{{6}{4}{A multidimensional polynomial sequence}{equation.2.6}{}}
\newlabel{mk:1}{{2}{4}{A multidimensional polynomial sequence}{table.3}{}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces  The triangles $(T_s^k(n))$ and the sequences $(c_k(n))$}}{5}{table.1}}
\newlabel{table:1}{{1}{5}{The triangles $(T_s^k(n))$ and the sequences $(c_k(n))$}{table.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces  First rows of $(T_s^k(2))$ and $(T_s^k(3))$ and the links to OEIS}}{5}{table.2}}
\newlabel{table:2}{{2}{5}{First rows of $(T_s^k(2))$ and $(T_s^k(3))$ and the links to OEIS}{table.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces First elements of $(c_{2k}(n))$, ($n=2,\dots  ,7$) and the links to OEIS}}{6}{table.3}}
\newlabel{table:3}{{3}{6}{First elements of $(c_{2k}(n))$, ($n=2,\dots ,7$) and the links to OEIS}{table.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Connection-like identities}{6}{section.3}}
\newlabel{sec:3}{{3}{6}{Connection-like identities}{section.3}{}}
\newlabel{Lemma1}{{1}{6}{}{theorem.1}{}}
\newlabel{eq:6}{{7}{6}{}{equation.3.7}{}}
\newlabel{As}{{8}{6}{}{equation.3.8}{}}
\citation{FalcaoMalonek2012b}
\citation{MalonekFalcao2007}
\citation{FalcaoCruzMalonek2006}
\newlabel{Th3.5}{{9}{7}{Connection-like identities}{equation.3.9}{}}
\newlabel{Theorem1}{{2}{7}{}{theorem.2}{}}
\newlabel{Mk}{{10}{7}{}{equation.3.10}{}}
\newlabel{Lemma2}{{3}{8}{}{theorem.3}{}}
\newlabel{Theorem2}{{5}{8}{}{theorem.5}{}}
\newlabel{sistema2}{{11}{8}{}{equation.3.11}{}}
\newlabel{Nk}{{12}{8}{}{equation.3.12}{}}
\newlabel{sistema3}{{13}{8}{}{equation.3.13}{}}
\newlabel{NNk}{{14}{8}{}{equation.3.14}{}}
\newlabel{Theorem3}{{6}{9}{}{theorem.6}{}}
\newlabel{t1}{{15}{9}{}{equation.3.15}{}}
\newlabel{sigma}{{16}{9}{}{equation.3.16}{}}
\newlabel{Theorem4}{{7}{10}{}{theorem.7}{}}
\newlabel{ck:2}{{17}{10}{}{equation.3.17}{}}
\newlabel{Theorem5}{{9}{11}{}{theorem.9}{}}
\citation{MianaOhtsukaRomero2017}
\@writefile{toc}{\contentsline {section}{\numberline {4}A family of Pascal trapezoids}{12}{section.4}}
\newlabel{sec:4}{{4}{12}{A family of Pascal trapezoids}{section.4}{}}
\newlabel{Theorem6}{{10}{12}{Pascal recurrence}{theorem.10}{}}
\newlabel{rr}{{18}{12}{Pascal recurrence}{equation.4.18}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces The matrices $N_k$, $\mathaccentV {widetilde}3C7N_k=N_k^{-1}$, and the vectors $\mathbf  T_k(n)$, $\mathbf  C_k(n)$, $(k=1,\dots  ,4)$}}{13}{table.4}}
\newlabel{table:4}{{4}{13}{The matrices $N_k$, $\widetilde N_k=N_k^{-1}$, and the vectors $\mathbf T_k(n)$, $\mathbf C_k(n)$, $(k=1,\dots ,4)$}{table.4}{}}
\newlabel{bc}{{19}{13}{Pascal recurrence}{equation.4.19}{}}
\newlabel{iv}{{20}{13}{Pascal recurrence}{equation.4.20}{}}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Triangles associated with $\sigma _{i,j}^{k}$, $(i=0,\dots  , 3)$}}{14}{table.5}}
\newlabel{table:5}{{5}{14}{Triangles associated with $\sigma _{i,j}^{k}$, $(i=0,\dots , 3)$}{table.5}{}}
\citation{Gould}
\newlabel{Property1}{{11}{15}{}{theorem.11}{}}
\newlabel{Property2}{{12}{15}{}{theorem.12}{}}
\bibcite{AcetoMalonekTomaz2017}{1}
\newlabel{expansion}{{21}{16}{A family of Pascal trapezoids}{equation.4.21}{}}
\newlabel{Property3}{{13}{16}{}{theorem.13}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Acknowledgments}{16}{section.5}}
\bibcite{BockGurlebeck2010}{2}
\bibcite{CacaoMalonek2008}{3}
\bibcite{CacaoFalcaoMalonek2011}{4}
\bibcite{CacaoMalonek2011a}{5}
\bibcite{CacaoFalcaoMalonek2012}{6}
\bibcite{CacaoFalcaoMalonek2017}{7}
\bibcite{CacaoFalcaoMalonek2017a}{8}
\bibcite{CruzFalcaoMalonek2011}{9}
\bibcite{CruzFalcaoMalonek2014}{10}
\bibcite{Eelbode2012}{11}
\bibcite{FalcaoCruzMalonek2006}{12}
\bibcite{FalcaoMalonek2007}{13}
\bibcite{FalcaoMalonek2012b}{14}
\bibcite{Gould}{15}
\bibcite{GuerlebeckMalonek1999}{16}
\bibcite{Guerlebeck2009}{17}
\bibcite{Lavicka2010}{18}
\bibcite{Lavicka2012}{19}
\bibcite{Malonek2004}{20}
\bibcite{MalonekFalcao2007}{21}
\bibcite{MalonekFalcao2010}{22}
\bibcite{MalonekFalcao2011}{23}
\bibcite{MianaOhtsukaRomero2017}{24}
\bibcite{MoraisLe2011}{25}
\bibcite{OEIS}{26}