Minimum size blocking sets of certain line sets related to a conic in

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• 作者：Kamal L. Patra ^{klpatra@niser.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Binod K. Sahoo ; ^{bksahoo@niser.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Bikramaditya Sahu ^{bikram.sahu@niser.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Baer subplane ; Irreducible conic ; Blocking set
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 June 2016
• 年：2016
• 卷：339
• 期：6
• 页码：1716-1721
• 全文大小：372 K

文摘

Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si2.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=8de5f847d72d7a30f4a2776327ebe4ee" title="Click to view the MathML source">Eclass="mathContainer hidden">class="mathCode">$\mathbb{E}$ (respectively; class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si3.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=5ca220a01bfe514f31ad3f8d0f57fdab" title="Click to view the MathML source">Tclass="mathContainer hidden">class="mathCode">$\mathbb{T}$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si4.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=d856cf96beccc3734e24ecd736e9258c" title="Click to view the MathML source">Sclass="mathContainer hidden">class="mathCode">$\mathbb{S}$) denote the set of all lines which are external (respectively; tangent, secant) to an irreducible conic in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si1.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=30258dcca7c9287c400dd56124421ac7" title="Click to view the MathML source">PG(2,q)class="mathContainer hidden">class="mathCode">$PG(2,q)$. We give a brief survey of the known results regarding the minimum size class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si6.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=ac23928cacd508fe231f9b471c2eeaf0" title="Click to view the MathML source">Lclass="mathContainer hidden">class="mathCode">$\mathbb{L}$-blocking sets of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si1.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=30258dcca7c9287c400dd56124421ac7" title="Click to view the MathML source">PG(2,q)class="mathContainer hidden">class="mathCode">$PG(2,q)$ for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si8.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=1f59de0f7754e852d4e3cb2ef3c11230" title="Click to view the MathML source">L∈{E,S,T∪E,T∪S}class="mathContainer hidden">class="mathCode">$\mathbb{L}\in \{\mathbb{E},\mathbb{S},\mathbb{T}\cup \mathbb{E},\mathbb{T}\cup \mathbb{S}\}$ and study the other two cases when class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si9.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=17e2d79a629cc92a45698ba7549ccabb" title="Click to view the MathML source">L=Tclass="mathContainer hidden">class="mathCode">$\mathbb{L}=\mathbb{T}$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X16000200&_mathId=si10.gif&_user=111111111&_pii=S0012365X16000200&_rdoc=1&_issn=0012365X&md5=8d28c057a7cc3d5ad0576de0c1b39e7c" title="Click to view the MathML source">E∪Sclass="mathContainer hidden">class="mathCode">$\mathbb{E}\cup \mathbb{S}$.