Browse latest articles

On the shelling antimatroids of split graphs


Chordal graph shelling antimatroids have received little attention with regard to their combinatorial properties and related optimization problems, as compared to the case of poset shelling antimatroids. Here we consider a special case of these antimatroids, namely the split graph shelling […]


Volume: Vol 19 no. 1
Section: Combinatorics
Published on: March 24, 2017
Wilf classification of triples of 4-letter patterns II


This is the second of two papers in which we determine all 242 Wilf classes of triples of 4-letter patterns by showing that there are 32 non-singleton Wilf classes. There are 317 symmetry classes of triples of 4-letter patterns and after computer calculation of initial terms, the problem reduces to […]


Volume: Vol 19 no. 1
Section: Combinatorics
Published on: March 24, 2017
Wilf classification of triples of 4-letter patterns I


This is the first of two papers in which we determine all 242 Wilf classes of triples of 4-letter patterns by showing that there are 32 non-singleton Wilf classes. There are 317 symmetry classes of triples of 4-letter patterns and after computer calculation of initial terms, the problem reduces to […]


Volume: Vol 19 no. 1
Section: Combinatorics
Published on: March 24, 2017
A class of symmetric difference-closed sets related to commuting involutions
Authors: Campbell, John.


Recent research on the combinatorics of finite sets has explored the structure of symmetric difference-closed sets, and recent research in combinatorial group theory has concerned the enumeration of commuting involutions in $S_{n}$ and $A_{n}$. In this article, we consider an interesting combination […]


Volume: Vol 19 no. 1
Section: Combinatorics
Published on: March 23, 2017
Permutation Pattern matching in (213, 231)-avoiding permutations


Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231. For the special case where […]


Volume: Vol. 18 no. 2, Permutation Patterns 2015
Section: Permutation Patterns
Published on: March 22, 2017
The Existence of Planar Hypotraceable Oriented Graphs


A digraph is \emph{traceable} if it has a path that visits every vertex. A digraph $D$ is \emph{hypotraceable} if $D$ is not traceable but $D-v$ is traceable for every vertex $v\in V(D)$. It is known that there exists a planar hypotraceable digraph of order $n$ for every $n\geq 7$, but no examples […]


Volume: Vol 19 no. 1
Section: Graph Theory
Published on: March 16, 2017
A characterization of trees with equal 2-domination and 2-independence numbers


A set $S$ of vertices in a graph $G$ is a $2$-dominating set if every vertex of $G$ not in $S$ is adjacent to at least two vertices in $S$, and $S$ is a $2$-independent set if every vertex in $S$ is adjacent to at most one vertex of $S$. The $2$-domination number $\gamma_2(G)$ is the minimum […]


Volume: Vol 19 no. 1
Section: Graph Theory
Published on: March 9, 2017
A New Game Invariant of Graphs: the Game Distinguishing Number


The distinguishing number of a graph $G$ is a symmetry related graph invariant whose study started two decades ago. The distinguishing number $D(G)$ is the least integer $d$ such that $G$ has a $d$-distinguishing coloring. A distinguishing $d$-coloring is a coloring […]


Volume: Vol 19 no. 1
Section: Graph Theory
Published on: March 2, 2017
Descent c-Wilf Equivalence


Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of left-to-right minima of $\sigma$. For any […]


Volume: Vol. 18 no. 2, Permutation Patterns 2015
Section: Permutation Patterns
Published on: March 2, 2017
Right-jumps and pattern avoiding permutations


We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding permutations. We characterize the elements of the basis of this […]


Volume: Vol. 18 no. 2, Permutation Patterns 2015
Section: Permutation Patterns
Published on: February 10, 2017