<?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>S0034-74262022000100063</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v56n1.105617</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Sizes of flats of cycle matroids of complete graphs]]></article-title>
<article-title xml:lang="es"><![CDATA[Los tamaños de los cerrados de la matroide gráfica del grafo completo]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kriel]]></surname>
<given-names><![CDATA[Christo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mphako-Banda]]></surname>
<given-names><![CDATA[Eunice]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,University of the Witwatersrand  ]]></institution>
<addr-line><![CDATA[Johannesburg ]]></addr-line>
<country>South Africa</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>63</fpage>
<lpage>75</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262022000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262022000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262022000100063&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We show that the problem of counting the number of flats of size k for a cycle matroid of a complete graph is equivalent to the problem of counting the number of partitions of an integer k into triangular numbers. In addition, we give some values of k such that there is no flat of size k in a cycle matroid of a complete graph of order n. Finally, we give a minimum bound for the number of values, k, for which there are no flats of size k in the given cycle matroid.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Demostraremos que el problema de contar los conjuntos cerrados de tamaño k de la matroide gráfica de un grafo completo es equivalente al problema de contar las particiones de un entero k en números triangulares. Adicionalmente, daremos unos valores de k tales que no existe ningún cerrado de tamaño k en la matroide gráfica de un grafo completo de orden n. Finalmente, daremos una cota inferior para el número de valores k para los cuales no existe ningún cerrado de tamaño k en la matroide gráfica.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Compositions]]></kwd>
<kwd lng="en"><![CDATA[cycle matroid]]></kwd>
<kwd lng="en"><![CDATA[flats]]></kwd>
<kwd lng="en"><![CDATA[triangular number partitions]]></kwd>
<kwd lng="en"><![CDATA[bad colouring]]></kwd>
<kwd lng="es"><![CDATA[Composiciones]]></kwd>
<kwd lng="es"><![CDATA[matroide]]></kwd>
<kwd lng="es"><![CDATA[particiones de números triangulares]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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</back>
</article>
