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Benjamini--Schramm continuity of root moments of graph polynomials
Graph polynomial of exponential type Tutte polynomial Chromatic polynomial Benjamini–Schramm convergence Sokal bound
2012/4/18
Recently, M.\ Ab\'ert and T.\ Hubai studied the following problem. The chromatic measure of a finite simple graph is defined to be the uniform distribution on its chromatic roots. Ab\'ert and Hubai pr...
A sharp upper bound for the rainbow 2-connection number of 2-connected graphs
rainbow edge-coloring rainbow k-connection number 2-connected graph ear decomposition
2012/4/18
A path in an edge-colored graph is called {\em rainbow} if no two edges of it are colored the same. For an $\ell$-connected graph $G$ and an integer $k$ with $1\leq k\leq \ell$, the {\em rainbow $k$-c...
Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whene...
The local $h$-vector of the cluster subdivision of a simplex
Local h-vector barycentric subdivision cluster complex cluster subdivision
2012/4/18
The cluster complex $\Delta (\Phi)$ is an abstract simplicial complex, introduced by Fomin and Zelevinsky for a finite root system $\Phi$. The positive part of $\Delta (\Phi)$ naturally defines a simp...
We describe two different approaches to making systematic classifications of plane lattice polygons, and recover the toric codes they generate, over small fields, where these match or exceed the best ...
Grid Representations and the Chromatic Number
Grid Representations the Chromatic Number Combinatorics
2012/4/17
A grid drawing of a graph maps vertices to grid points and edges to line segments that avoid grid points representing other vertices. We show that there is a number of grid points that some line segme...
On Zudilin's q-question about Schmidt's problem
Schmidt’s problem q-binomial coefficients q-Pfaff-Saalschutz identity
2012/4/17
For any integer $r\geqslant 2$, using the $q$-Pfaff-Saalsch\"utz identity, we prove that there exists a (unique) sequence of Laurent polynomials $\{b^{(r)}_k(q)\}_{k=0}^\infty$ in $q$ with nonnegative...
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem ...
Lattice multi-polygons
Lattice polygon twelve-point theorem Pick’s formula Ehrhart polynomial toric topology
2012/4/17
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\Z^2$. We first prove a formula on...
Pencils of lines in generalized Laguerre spaces
Combinatorics Multidimensional Laguerre spaces subspaces pencils Grassmann spaces
2012/4/17
In the paper we characterize subspaces and pencils of lines of generalized (and multidimensional) Laguerre spaces and we consider definability of the structure of "conic" pencils in the Grassmann spac...
Divided Differences of Multivariate Implicit Functions
Divided Differences Multivariate Implicit Functions Numerical Analysis Combinatorics
2012/3/1
Under general conditions, the equation $g(x^1, ..., x^q, y) = 0$ implicitly defines $y$ locally as a function of $x^1, ..., x^q$. In this article, we express divided differences of $y$ in terms of div...
Separation probabilities for products of permutations
Separation probabilities products permutations fixed cycle types
2012/3/1
We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements...
The Minimum Number of Dependent Arcs and a Related Parameter of Generalized Mycielski Graphs
acyclic orientation dependent arc source-reversal cover graph generalized Mycielski graph
2012/3/1
Let D be an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let m(G) denote the minimum number of dependent arcs over all acyclic orientations of...
Quaternary Constant-Composition Codes with Weight Four and Distances Five or Six
Quaternary Constant-Composition Codes Weight Four Distances Five or Six
2012/3/1
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their construction...
We give a realization of the infinity crystal for affine sl(2) using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito's characterization of the infin...