<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262022000100001</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v56n1.105611</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Faà di Bruno Hopf algebras]]></article-title>
<article-title xml:lang="es"><![CDATA[Álgebras de Hopf de Faà di Bruno]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Figueroa]]></surname>
<given-names><![CDATA[Héctor]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Várilly]]></surname>
<given-names><![CDATA[Joseph C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gracia-Bondía]]></surname>
<given-names><![CDATA[José M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[San José ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Zaragoza  ]]></institution>
<addr-line><![CDATA[Zaragoza ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<volume>56</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>12</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262022000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262022000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262022000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This is a short review on the Faá di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure provides, among several other things, a short proof of the Lie-Scheffers theorem, and relates the Lagrange inversion formulas with antipodes. It is also the maximal commutative Hopf subalgebra of the one used by Connes and Moscovici to study diffeomorphisms in a noncommutative geometry setting. The link of Faa di Bruno formulas with the theory of set partitions is developed in some detail.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Esta es una reseña corta sobre las fórmulas de Faá di Bruno, implementando composición de funciones analíticas reales, y algunas álgebras de Hopf asociadas a dichas fórmulas. Entre otras cosas, tal estructura permite una demostración corta del teorema de Lie y Scheffers, y establece la relación entre las fórmulas de inversión de Lagrange y los antípodas. Esta álgebra de Hopf es la subálgebra conmutativa maximal del álgebra introducida por Connes y Moscovici para estudiar difeomorfismos en el marco de la geometría no conmutativa. Asimismo, desarrollamos con cierto detalle el vínculo entre las fórmulas de Faà di Bruno y la teoría de particiones de conjuntos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Faá di Bruno formula]]></kwd>
<kwd lng="en"><![CDATA[Hopf algebras]]></kwd>
<kwd lng="en"><![CDATA[partitions]]></kwd>
<kwd lng="es"><![CDATA[Fórmula de Faà di Bruno]]></kwd>
<kwd lng="es"><![CDATA[álgebras de Hopf]]></kwd>
<kwd lng="es"><![CDATA[particiones]]></kwd>
</kwd-group>
</article-meta>
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