http://www.combinatorics.org/ojs/index.php/eljc/issue/feedThe Electronic Journal of Combinatorics2015-04-16T11:08:59+10:00André Kündgenakundgen@csusm.eduOpen Journal Systems<p>The copyright of published papers remains with the authors. We only require your agreement that we publish it, as described in the following publication release agreement:</p><ol><li>This is an agreement between the Electronic Journal of Combinatorics (the "Journal"), and the copyright owner (the "Owner") of a work (the "Work") to be published in the Journal.</li><li>The Owner warrants that s/he has the full power and authority to enter into this Agreement and to grant the rights granted in this Agreement.</li><li>The Owner hereby grants to the Journal a worldwide, irrevocable, royalty free license to publish or distribute the Work, to enter into arrangements with others to publish or distribute the Work, and to archive the Work.</li><li>The Owner agrees that further publication of the Work, with the same or substantially the same content as appears in the Journal, will include an acknowledgement of prior publication in the Journal.</li></ol><p>The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with <em>very high standards,</em> publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems. The journal is <em>completely free</em> for both authors and readers. Authors retain the copyright of their articles. Articles published in E-JC are reviewed on MathSciNet and ZBMath, and are indexed by Web of Science. The latest papers are always available by clicking on the tab marked "Current" near the top of the page. You can also locate papers using the search facility on the right hand side of this page.</p><p>E-JC was founded in 1994 by Herbert S. Wilf and Neil Calkin, making it one of the oldest electronic journals.</p>http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i2p1A Note on Coloring Vertex-Transitive Graphs2015-04-16T11:08:59+10:00Daniel W. Cranstondcranston@vcu.eduLandon Rabernlandon.rabern@gmail.com<p>We prove bounds on the chromatic number $\chi$ of a vertex-transitive graph in terms of its clique number $\omega$ and maximum degree $\Delta$. We conjecture that every vertex-transitive graph satisfies $\chi \le \max \{\omega, \left\lceil\frac{5\Delta + 3}{6}\right\rceil\}$, and we prove results supporting this conjecture. Finally, for vertex-transitive graphs with $\Delta \ge 13$ we prove the Borodin<span>–</span>Kostochka conjecture, i.e., $\chi\le\max\{\omega,\Delta-1\}$.</p>2015-04-14T00:00:00+10:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i2p2Equipopularity Classes in the Separable Permutations2015-04-14T01:16:09+10:00Michael Albertmalbert@cs.otago.ac.nzCheyne Hombergercheyne.homberger@gmail.comJay Pantonejay.pantone@gmail.com<p>When two patterns occur equally often in a set of permutations, we say that these patterns are equipopular. Using both structural and analytic tools, we classify the equipopular patterns in the set of separable permutations. In particular, we show that the number of equipopularity classes for length $n$ patterns in the separable permutations is equal to the number of partitions of $n-1$.</p>2015-04-14T00:00:00+10:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i2p3Roudneff's Conjecture for Lawrence Oriented Matroids2015-04-14T01:16:09+10:00Luis Pedro Montejanolpmontejano@gmail.comJorge Luis Ramírez-Alfonsínjramirez@um2.frJ.-P. Roudneff has conjectured that every arrangement of $n\ge 2d+1\ge 5$ (pseudo) hyperplanes in the real projective space $\mathbb{P}^d$ has at most $\sum_{i=0}^{d-2} \binom{n-1}{i}$ cells bounded by each hyperplane. In this note, we show the validity of this conjecture for arrangements arising from Lawrence oriented matroids.2015-04-14T00:00:00+10:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i2p4Young Diagrams and Intersection Numbers for Toric Manifolds associated with Weyl Chambers2015-04-14T01:16:09+10:00Hiraku Abehirakuabe@globe.ocn.ne.jp<p>We study intersection numbers of invariant divisors in the toric manifold associated with the fan determined by the collection of Weyl chambers for each root system of classical type and of exceptional type $G_2$. We give a combinatorial formula for intersection numbers of certain subvarieties which are naturally indexed by elements of the Weyl group. These numbers describe the ring structure of the cohomology of the toric manifold.</p>2015-04-14T00:00:00+10:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i2p5Permutations Destroying Arithmetic Structure2015-04-14T01:16:09+10:00Veselin Jungićvjungic@sfu.caJulian Sahasrabudhejulian.sahasra@gmail.com<pre>Given a linear form <span>$C_1X_1 + \cdots + C_nX_n$</span>, with coefficients in the integers, we characterize exactly the countably infinite <span>abelian</span> groups <span>$G$</span> for which there exists a permutation <span>$f$</span> that maps all solutions <span>$(\alpha_1, \ldots , \alpha_n) \in G^n$</span> (with the <span>$\alpha_i$</span> not all equal) to the equation <span>$C_1X_1 + \cdots + C_nX_n = 0 $</span> to non-solutions. This generalises a result of <span>Hegarty</span> about permutations of an <span>abelian</span> group avoiding arithmetic progressions. We also study the finite version of the problem suggested by <span>Hegarty</span>. We show that the number of permutations of <span>$\mathbb{Z}/p\mathbb{Z}$</span> that map all 4-term arithmetic progressions to non-progressions, is asymptotically <span>$e^{-1}p!$</span>.</pre>2015-04-14T00:00:00+10:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i2p6Flag-Transitive Non-Symmetric 2-Designs with $(r,\lambda)=1$ and Alternating Socle2015-04-16T11:07:05+10:00Shenglin Zhouslzhou@scut.edu.cnYajie Wangwangyajie8786@163.comThis paper deals with flag-transitive non-symmetric 2-designs with $(r,\lambda)=1$. We prove that if $\mathcal D$ is a non-trivial non-symmetric $2$-$(v,k,\lambda)$ design with $(r,\lambda)=1$ and $G\leq Aut(\mathcal D)$ is flag-transitive with $Soc(G)=A_n$ for $n\geq 5$, then $\mathcal D$ is a $2$-$(6,3,2)$ design, the projective space $PG(3,2)$, or a $2$-$(10,6,5)$ design.2015-04-14T00:00:00+10:00