<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332021000100039</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v28i1.33773</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Existence conditions for k-barycentric olson constant]]></article-title>
<article-title xml:lang="es"><![CDATA[Condiciones de existencia para la constante de olson k-baricéntrica]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Marchan]]></surname>
<given-names><![CDATA[Luz]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ordaz]]></surname>
<given-names><![CDATA[Oscar]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Salazar]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Villarroel]]></surname>
<given-names><![CDATA[Felicia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Escuela Superior Politécnica del Litoral Facultad de Ciencias Naturales Departamento de Matemáticas]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Ecuador</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Central de Venezuela Departamento de Matemáticas y Laboratorio LaTecS; Centro ISYS Facultad de Ciencias]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Venezuela</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Oriente  Departamento de Matemáticas; Núcleo Sucre]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Venezuela</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Oriente  Departamento de Matemáticas; Núcleo Sucre]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Venezuela</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<volume>28</volume>
<numero>1</numero>
<fpage>39</fpage>
<lpage>53</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332021000100039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332021000100039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332021000100039&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Let (G, +) be a finite abelian group and 3 &#8804; k &#8804; |G| a positive integer. The k-barycentric Olson constant denoted by BO(k, G) is defined as the smallest integer &#8467; such that each set A of G with |A| = &#8467; contains a subset with k elements {a1, . . . , ak} satisfying a1 + · · · + ak = kaj for some 1 &#8804; j &#8804; k. We establish some general conditions on G assuring the existence of BO(k, G) for each 3 &#8804; k &#8804; |G|. In particular, from our results we can derive the existence conditions for cyclic groups and for elementary p-groups p &#8805; 3. We give a special treatment over the existence condition for the elementary 2-groups.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Sean (G, +) un grupo abeliano finito y 3 &#8804; k &#8804; |G| un entero positivo. La constante de Olson k-baricéntrica, denotada por BO(k, G), se define como el menor entero positivo &#8467; tal que todo conjunto A de G con |A| = &#8467; contiene un subconjunto con k elementos {a1, . . . , ak} que satisface a1+· · ·+ak = kaj para algún 1 &#8804; j &#8804; k. Establecemos algunas condiciones generales sobre G asegurando la existencia de BO(k, G) para cada 3 &#8804; k &#8804; |G|. En particular, a partir de nuestros resultados podemos determinar las condiciones de existencia para los grupos cíclicos y para los p-grupos elementales con p &#8805; 3. Damos un tratamiento especial a la condición de existencia para los 2-grupos elementales.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[finite abelian group]]></kwd>
<kwd lng="en"><![CDATA[zero-sum problem]]></kwd>
<kwd lng="en"><![CDATA[baricentric-sum problem]]></kwd>
<kwd lng="en"><![CDATA[Davenport constant]]></kwd>
<kwd lng="en"><![CDATA[k-barycentric Olson constant.]]></kwd>
<kwd lng="es"><![CDATA[grupos abelianos finitos]]></kwd>
<kwd lng="es"><![CDATA[problemas de suma-cero]]></kwd>
<kwd lng="es"><![CDATA[problemas de suma baricéntricas]]></kwd>
<kwd lng="es"><![CDATA[constante de Davenport]]></kwd>
<kwd lng="es"><![CDATA[constante k-baricéntrica de Olson.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Bierbrauer]]></given-names>
</name>
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Edel.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bounds on affine caps]]></article-title>
<source><![CDATA[Journal of Combinatorial Designs]]></source>
<year>2002</year>
<volume>10</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>111-5</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Edel]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Ferret]]></given-names>
</name>
<name>
<surname><![CDATA[I]]></surname>
<given-names><![CDATA[Landjev]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Storme.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The classification of the largest caps in AG(5, 3)]]></article-title>
<source><![CDATA[Journal of Combinatorial Theory]]></source>
<year>2002</year>
<volume>99</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>95-110</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[W]]></surname>
<given-names><![CDATA[Gao]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Geroldinger.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On long minimal zero sequences in finite abelian groups]]></article-title>
<source><![CDATA[Periodica Mathematica Hungarica]]></source>
<year>1999</year>
<volume>38</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>179-211</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[W]]></surname>
<given-names><![CDATA[Gao]]></given-names>
</name>
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Thangadurai.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A variant of Kemnitz conjecture]]></article-title>
<source><![CDATA[Journal of Combinatorial Theory]]></source>
<year>2004</year>
<volume>107</volume>
<page-range>69-86</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Grynkiewicz.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A weighted Erdös-Ginzburg-Ziv theorem]]></article-title>
<source><![CDATA[Combinatorica]]></source>
<year>2006</year>
<volume>26</volume>
<page-range>445-53</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Hamidoune.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On weighted sums in abelian groups]]></article-title>
<source><![CDATA[Discrete Mathematics]]></source>
<year>1996</year>
<volume>162</volume>
<page-range>127-32</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Hill.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the largest size of cap in S5,3]]></article-title>
<source><![CDATA[Atti Accad. Naz. Lincei Rend.]]></source>
<year>1973</year>
<volume>54</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>378-84</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Hill.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Caps and codes]]></article-title>
<source><![CDATA[Discrete Mathematics]]></source>
<year>1978</year>
<volume>22</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>111-37</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Kemnitz.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On a lattice point probems]]></article-title>
<source><![CDATA[Ars Combinatoria]]></source>
<year>1983</year>
<volume>16b</volume>
<page-range>151-60</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[F]]></surname>
<given-names><![CDATA[Luca]]></given-names>
</name>
<name>
<surname><![CDATA[O]]></surname>
<given-names><![CDATA[Ordaz]]></given-names>
</name>
<name>
<surname><![CDATA[M,T]]></surname>
<given-names><![CDATA[Varela.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On barycentric constants]]></article-title>
<source><![CDATA[Revista de la Unión Matemática Argentina]]></source>
<year>2012</year>
<volume>53</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>1-12</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[L,E]]></surname>
<given-names><![CDATA[Marchan]]></given-names>
</name>
<name>
<surname><![CDATA[O]]></surname>
<given-names><![CDATA[Ordaz]]></given-names>
</name>
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Ramos]]></given-names>
</name>
<name>
<surname><![CDATA[W]]></surname>
<given-names><![CDATA[Schmid.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some exact values of the Harborth constant and its plus-minus weighted analogue]]></article-title>
<source><![CDATA[Arch. Math.]]></source>
<year>2013</year>
<volume>101</volume>
<page-range>501-12</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Mukhopadhyay.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lower bounds on mt(r, s)]]></article-title>
<source><![CDATA[Journal of Combinatorial Theory]]></source>
<year>1978</year>
<volume>25</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-13</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[O]]></surname>
<given-names><![CDATA[Ordaz]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Plagne]]></given-names>
</name>
<name>
<surname><![CDATA[W,A]]></surname>
<given-names><![CDATA[Schmid.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some remarks on barycentricsum problems over cyclic groups]]></article-title>
<source><![CDATA[European Journal of Combinatorics]]></source>
<year>2013</year>
<volume>34</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>1415-28</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[O]]></surname>
<given-names><![CDATA[Ordaz]]></given-names>
</name>
<name>
<surname><![CDATA[M,T]]></surname>
<given-names><![CDATA[Varela]]></given-names>
</name>
<name>
<surname><![CDATA[F]]></surname>
<given-names><![CDATA[Villarroel.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[k-barycentric Olson constant]]></article-title>
<source><![CDATA[Math. Reports]]></source>
<year>2009</year>
<volume>11</volume>
<numero>61</numero>
<issue>61</issue>
<page-range>33-45</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
