Search results for " Combinatoric"
showing 10 items of 299 documents
Ornamenti un Simetrijas: Ornamentālo Rakstu Zīmju Valoda (intervija ar Modri Tenisonu)
2010
Ornaments and Symmetry: Language of Signs of Ornamental Tracery (see interview with Modris Tenisons http://www.blip.tv/file/3173653) In his first interview Modris Tenisons explains language of ornamentalistic signs for national ornamental belts using his discovered law of sieve displacement, which gives base duality element in ornamentalistic signs, and routine how to generate 240 elements of signs from 10 “seeds of chaos” sufficient to produce all ornametal belts of first order. He tells also about his discoverd 16 sign alphabet, that does the same. Pirmajā mutvārdu liecinājumā Modris Tenisons stāsta par ornamentālo rakstu zīmju veidošanās likumsakarībām sakrustojot divu krāsu diegus audum…
Strong chromatic index of products of graphs
2007
Graphs and Algorithms
Local Normal Forms for First-Order Logic with Applications to Games and Automata
1999
Building on work of Gaifman [Gai82] it is shown that every first-order formula is logically equivalent to a formula of the form ∃ x_1,...,x_l, \forall y, φ where φ is r-local around y, i.e. quantification in φ is restricted to elements of the universe of distance at most r from y. \par From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler, one of the two players. This makes proofs of the existence of a winning strategy for the duplicator, the other player, easier and can thus simplify inexpressibility proofs. \par As another application, automata mode…
Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes
2006
A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…
Gray code for permutations with a fixed number of cycles
2007
AbstractWe give the first Gray code for the set of n-length permutations with a given number of cycles. In this code, each permutation is transformed into its successor by a product with a cycle of length three, which is optimal. If we represent each permutation by its transposition array then the obtained list still remains a Gray code and this allows us to construct a constant amortized time (CAT) algorithm for generating these codes. Also, Gray code and generating algorithm for n-length permutations with fixed number of left-to-right minima are discussed.
Radio Labelings of Distance Graphs
2013
A radio $k$-labeling of a connected graph $G$ is an assignment $c$ of non negative integers to the vertices of $G$ such that $$|c(x) - c(y)| \geq k+1 - d(x,y),$$ for any two vertices $x$ and $y$, $x\ne y$, where $d(x,y)$ is the distance between $x$ and $y$ in $G$. In this paper, we study radio labelings of distance graphs, i.e., graphs with the set $\Z$ of integers as vertex set and in which two distinct vertices $i, j \in \Z$ are adjacent if and only if $|i - j| \in D$.
Some new Hadamard designs with 79 points admitting automorphisms of order 13 and 19
2001
Abstract We have proved that there exists at least 2091 mutually nonisomorphic symmetric (79,39,19)-designs. In particular, 1896 of them admit an action of the nonabelian group of order 57, and an additional 194 an action of the nonabelian group of order 39.
On the graded identities and cocharacters of the algebra of 3×3 matrices
2004
Abstract Let M2,1(F) be the algebra of 3×3 matrices over an algebraically closed field F of characteristic zero with non-trivial Z 2 -grading. We study the graded identities of this algebra through the representation theory of the hyperoctahedral group Z 2 ∼S n . After splitting the space of multilinear polynomial identities into the sum of irreducibles under the Z 2 ∼S n -action, we determine all the irreducible Z 2 ∼S n -characters appearing in this decomposition with non-zero multiplicity. We then apply this result in order to study the graded cocharacter of the Grassmann envelope of M2,1(F). Finally, using the representation theory of the general linear group, we determine all the grade…
Hopf bifurcation at infinity for planar vector fields
2007
We study, from a new point of view, families of planar vector fields without singularities $ \{ X_{\mu}$  :  $-\varepsilon < \mu < \varepsilon\} $ defined on the complement of an open ball centered at the origin such that, at $\mu=0$, infinity changes from repellor to attractor, or vice versa. We also study a sort of local stability of some $C^1$ planar vector fields around infinity.
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals
2018
The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of contai…