Related papers: Confluence in Labeled Chip-Firing
We have studied systematically the influence of particle-hole symmetric and asymmetric kinetic terms on the ordered phases that we may observe competing or coexisting in a tetragonal system. We show that there are precise patterns of…
We study the pairing correlations in a finite Fermi system from quantum entanglement point of view. We investigate the relation between the order parameter, which has been introduced recently to describe both finite and infinite…
In this paper, we report an optimized union-find (UF) algorithm that can label the connected components on a 2D image efficiently by employing the GPU architecture. The proposed method contains three phases: UF-based local merge, boundary…
A vertex ordering of a graph $G$ is a bijection $\pi\colon\{1,\dots,|V(G)|\}\to V(G)$. It is successive if the induced subgraph $G[v_{\pi(1)},\dots,v_{\pi(k)}]$ is connected for each $k$. Lixing Fang, Hao Huang, J\'anos Pach, G\'abor…
A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has…
In 1992, Bitar and Goles introduced the parallel chip-firing game on undirected graphs. Two years later, Prisner extended the game to directed graphs. While the properties of parallel chip-firing games on undirected graphs have been…
Suppose there are $n$ harmonic pencils of lines given in the plane. We are interested in the question whether certain triples of these lines are concurrent or if triples of intersection points of these lines are collinear, provided that we…
We generalize the work of Fomin, Greene, Reiner, and Shimozono on balanced labellings in two directions: (1) we define the diagrams of affine permutations and the balanced labellings on them; (2) we define the set-valued version of the…
Let X and Y be CW-complexes, U be an abelian group, and f:[X,Y]->U be a map (a homotopy invariant). We say that f has order at most r if the characteristic function of the r'th Cartesian power of the graph of a continuous map a:X->Y…
We settle a conjecture of B\'ona regarding the log-concavity of a certain statistic on parking functions by utilizing recent log-concavity results on matroids. This result allows us to also prove that connected, labeled graphs graded by…
A clutter is \emph{$k$-wise intersecting} if every $k$ members have a common element, yet no element belongs to all members. We conjecture that, for some integer $k\geq 4$, every $k$-wise intersecting clutter is non-ideal. As evidence for…
Even before the experimental discovery of spin- and charge-stripe order in La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and La$_{2-x}$Ba$_x$CuO$_4$ at x = 1/8, stripe formation was predicted from theoretical considerations. Nevertheless, a consistent…
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and they proved two partition bijections involving these…
Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present…
An unsplittable multiflow routes the demand of each commodity along a single path from its source to its sink node. As our main result, we prove that in series-parallel digraphs, any given multiflow can be expressed as a convex combination…
We settle affirmatively a conjecture posed in [S. M. Hegde, Set colorings of graphs, European Journal of Combinatorics 30 (4) (2009), 986--995]: If some subsets of a set X are assigned injectively to all vertices of a complete bipartite…
There are a number of well-known problems and conjectures about partitioning graphs to satisfy local constraints. For example, the majority colouring conjecture of Kreutzer, Oum, Seymour, van der Zypen and Wood states that every directed…
Let $B$ and $R$ be point sets (of {\em blue} and {\em red} points, respectively) in the plane, such that $P:=B\cup R$ is in general position, and $|P|$ is even. A line $\ell$ is {\em balanced} if it spans one blue and one red point, and on…
A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The…
We study uniformity conditions for parameterized Boolean circuit families. Uniformity conditions require that the infinitely many circuits in a circuit family are in some sense easy to construct from one shared description. For shallow…