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The Minor inequalities in the description of the Set Covering Polyhedron of Circulant Matrices
polyhedral combinatorics set covering circulant matrices Combinatorics
2012/6/25
In this work we give a complete description of the set covering polyhedron of circulant matrices $C^k_{sk}$ with $s = 2,3$ and $k\geq 3 $ by linear inequalities. In particular, we prove that every non...
We prove that every claw-free graph $G$ that doesn't contain a clique on $\Delta(G) \geq 9$ vertices can be $\Delta(G) - 1$ colored.
Combinatorial study of colored Hurwitz polyzetas
Combinatorial study colored Hurwitz polyzetas Combinatorics
2012/6/25
A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyz\^etas. The combinatorial aspects of the products and c...
A new approach to the results of Kovari, Sos, and Turan concerning rectangle-free subsets of the grid
Turan concerning rectangle-free subsets of the grid Combinatorics
2012/6/21
For positive integers $m$ and $n$, define $f(m,n)$ to be the smallest integer such that any subset $A$ of the $m \times n$ integer grid with $|A| \geq f(m,n)$ contains a rectangle; that is, there are ...
Permutations all of whose patterns of a given length are distinct
Permutations a given length distinct Combinatorics
2012/6/21
For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation \sigma \in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \lfloor \sqrt{2k-3}...
A Method for Obtaining Generating Function for Central Coefficients of Triangles
Obtaining Generating Function Central Coefficients of Triangles Combinatorics
2012/6/21
We consider problems of obtaining a generating function for the central coefficients of triangle $T(n,k)$, which is given by expression $[xG(x)]^k=\sum_{n\geqslant k} T(n,k)x^n$, $G(0)\neq 0$. We prov...
This note deals with the relationship between the total number of $k$-walks in a graph, and the sum of the $k$-th powers of its vertex degrees. In particular, it is shown that the the number of all $k...
The set of Dyck paths of length $2n$ inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution o...
Determination of Integral Cayley Graphs on Finite Abelian Groups
abelian group character cayley graph integral graph
2012/6/21
A graph is integral means that all its eigenvalues are integers. In this note, we determine all the integral Cayley graphs on finite abelian groups. Moreover, we calculate the the number of integral C...
We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite p...
We present a new approach for counting trees, and we apply it to count multitype Cayley trees and to prove the multivariate Lagrange inversion formula. The gist of our approach is to exploit the symme...
Enumerations of finite topologies associated with a finite graph
Enumerations of finite topologies finite graph Combinatorics
2012/6/19
The number of topologies and non-homeomorphic topologies on a fixed finite set are now known up to $n=18$, $n=16$ but still no complete formula yet (Sloane). There are one to one correspondence among ...
Mutually unbiased bases as submodules and subspaces
Mutually unbiased bases submodules and subspaces Combinatorics
2012/6/19
Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most o...
Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this...
The Sorting Index and Permutation Codes
Permutation statistics Mahonian statistics Coxeter groups Set-valued statistics Bijections
2012/6/19
In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced ...