http://www.combinatorics.org/ojs/index.php/eljc/issue/feedThe Electronic Journal of Combinatorics2015-01-02T11:36:01+11:00André 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/v22i1p1Periodic Rigidity on a Variable Torus Using Inductive Constructions2015-01-02T11:36:01+11:00Anthony Nixona.nixon@lancaster.ac.ukElissa Rosseross2@wpi.eduIn this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the language of gain graphs for the finite counterpart of a periodic graph. In this setting we employ variants of the Henneberg operations used frequently in rigidity theory.2015-01-02T00:00:00+11:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p2Evaluating the Numbers of some Skew Standard Young Tableaux of Truncated Shapes2015-01-02T11:36:01+11:00Ping Sunplsun@mail.neu.edu.cn<p>In this paper the number of standard Young tableaux (SYT) is evaluated by the methods of multiple integrals and combinatorial summations. We obtain the product formulas of the numbers of skew SYT of certain truncated shapes, including the skew SYT $((n+k)^{r+1},n^{m-1}) / (n-1)^r $ truncated by a rectangle or nearly a rectangle, the skew SYT of truncated shape $((n+1)^3,n^{m-2}) / (n-2) \backslash \; (2^2)$, and the SYT of truncated shape $((n+1)^2,n^{m-2}) \backslash \; (2)$.</p>2015-01-02T00:00:00+11:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p3Some Enumerations on Non-Decreasing Dyck Paths2015-01-02T11:36:01+11:00Éva Czabarkaczabarka@math.sc.eduRigoberto Flórezrigo.florez@citadel.eduLeandro Junesjunes@calu.eduWe construct a formal power series on several variables that encodes many statistics on non-decreasing Dyck paths. In particular, we use this formal power series to count peaks, pyramid weights, and indexed sums of pyramid weights for all non-decreasing Dyck paths of length $2n.$ We also show that an indexed sum on pyramid weights depends only on the size and maximum element of the indexing set.2015-01-02T00:00:00+11:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p4Group Homomorphisms as Error Correcting Codes2015-01-02T11:36:01+11:00Alan Guoaguo@mit.edu<p>We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups $G$ and $H$. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when $G$ is solvable or $H$ is nilpotent, in terms of the normal subgroup structure of $G$ as well as the prime divisors of $|G|$ and $|H|$. In particular, we show that in the above case, the distance is independent of the subgroup structure of $H$. We complement this by showing that, in general, the distance depends on the subgroup structure of $H$.</p>2015-01-02T00:00:00+11:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p5Vertically Symmetric Alternating Sign Matrices and a Multivariate Laurent Polynomial Identity2015-01-02T11:36:01+11:00Ilse Fischerilse.fischer@univie.ac.atIn 2007, the first author gave an alternative proof of the refined alternating sign matrix theorem by introducing a linear equation system that determines the refined ASM numbers uniquely. Computer experiments suggest that the numbers appearing in a conjecture concerning the number of vertically symmetric alternating sign matrices with respect to the position of the first 1 in the second row of the matrix establish the solution of a linear equation system similar to the one for the ordinary refined ASM numbers. In this paper we show how our attempt to prove this fact naturally leads to a more general conjectural multivariate Laurent polynomial identity. Remarkably, in contrast to the ordinary refined ASM numbers, we need to extend the combinatorial interpretation of the numbers to parameters which are not contained in the combinatorial admissible domain. Some partial results towards proving the conjectured multivariate Laurent polynomial identity and additional motivation why to study it are presented as well.2015-01-02T00:00:00+11:00http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p6On-Line Choice Number of Complete Multipartite Graphs: an Algorithmic Approach2015-01-02T11:36:01+11:00Fei-Huang Changfeihuang0228@gmail.comHong-Bin Chenandanchen@gmail.comJun-Yi Guojunyiguo@gmail.comYu-Pei Huangpei.am91g@nctu.edu.twThis paper studies the on-line choice number on complete multipartite graphs with independence number $m$. We give a unified strategy for every prescribed $m$. Our main result leads to several interesting consequences comparable to known results. (1) If $k_1-\sum_{p=2}^m\left(\frac{p^2}{2}-\frac{3p}{2}+1\right)k_p\geq 0$, where $k_p$ denotes the number of parts of cardinality $p$, then $G$ is on-line chromatic-choosable. (2) If $|V(G)|\leq\frac{m^2-m+2}{m^2-3m+4}\chi(G)$, then $G$ is on-line chromatic-choosable. (3) The on-line choice number of regular complete multipartite graphs $K_{m\star k}$ is at most<br />$\left(m+\frac{1}{2}-\sqrt{2m-2}\right)k$ for $m\geq 3$.2015-01-02T00:00:00+11:00