Search results for "Graph theory"
showing 10 items of 784 documents
Generating binary trees by Glivenko classes on Tamari lattices
2003
Using algebraic-theoretic results, we give an algorithm for generating binary trees within Glivenko classes in Tamari lattices. Tamari lattices are lattices of binary trees endowed by the well-known rotation transformation.
Fixed point properties and proximinality in Banach spaces
2009
Abstract In this paper we prove the existence of a fixed point for several classes of mappings (mappings admitting a center, nonexpansive mappings, asymptotically nonexpansive mappings) defined on the closed convex subsets of a Banach space satisfying some proximinality conditions. In particular, we derive a sufficient condition, more general than weak star compactness, such that if C is a bounded closed convex subset of l 1 satisfying this condition, then every nonexpansive mapping T : C → C has a fixed point.
Periodicity vectors for labelled trees
2003
AbstractThe concept of a periodicity vector is introduced in the context of labelled trees, and some new periodicity theorems are obtained. These results constitute generalizations of the classical periodicity theorem of Fine and Wilf for words. The concept of a tree congruence is also generalized and the isomorphism between the lattice of tree congruences and the lattice of unlabelled trees (prefix codes) is established.
Finite Groups with Only One NonLinear Irreducible Representation
2012
Let 𝕂 be an algebraically closed field. We classify the finite groups having exactly one irreducible 𝕂-representation of degree bigger than one. The case where the characteristic of 𝕂 is zero, was done by G. Seitz in 1968.
Polynomial codimension growth and the Specht problem
2017
Abstract We construct a continuous family of algebras over a field of characteristic zero with slow codimension growth bounded by a polynomial of degree 4. This is achieved by building, for any real number α ∈ ( 0 , 1 ) a commutative nonassociative algebra A α whose codimension sequence c n ( A α ) , n = 1 , 2 , … , is polynomially bounded and lim log n c n ( A α ) = 3 + α . As an application we are able to construct a new example of a variety with an infinite basis of identities.
Standard polynomials are characterized by their degree and exponent
2011
Abstract By the Giambruno–Zaicev theorem (Giambruno and Zaicev, 1999) [5] , the exponent exp ( A ) of a p.i. algebra A exists, and is always an integer. In Berele and Regev (2001) [2] it was shown that the exponent exp ( St n ) of the standard polynomial St n of degree n is not smaller than the exponent of any polynomial of degree n. Here it is proved that exp ( St n ) is strictly larger than the exponent of any other polynomial of degree n which is not a multiple of St n .
On computing the degree of convexity of polyominoes
2015
In this paper we present an algorithm which has as input a convex polyomino $P$ and computes its degree of convexity, defined as the smallest integer $k$ such that any two cells of $P$ can be joined by a monotone path inside $P$ with at most $k$ changes of direction. The algorithm uses space $O(m + n)$ to represent a polyomino $P$ with $n$ rows and $m$ columns, and has a running time $O(min(m; r k))$, where $r$ is the number of corners of $P$. Moreover, the algorithm leads naturally to a decomposition of $P$ into simpler polyominoes.
DEFECT THEOREMS FOR TREES
2000
We generalize different notions of a rank of a set of words to sets of trees. We prove that almost all of those ranks can be used to formulate a defect theorem. However, as we show, the prefix rank forms an exception.
Groups whose prime graph on conjugacy class sizes has few complete vertices
2012
Abstract Let G be a finite group, and let Γ ( G ) denote the prime graph built on the set of conjugacy class sizes of G. In this paper, we consider the situation when Γ ( G ) has “few complete vertices”, and our aim is to investigate the influence of this property on the group structure of G. More precisely, assuming that there exists at most one vertex of Γ ( G ) that is adjacent to all the other vertices, we show that G is solvable with Fitting height at most 3 (the bound being the best possible). Moreover, if Γ ( G ) has no complete vertices, then G is a semidirect product of two abelian groups having coprime orders. Finally, we completely characterize the case when Γ ( G ) is a regular …
A Newman property for BLD-mappings
2019
We define a Newman property for BLD-mappings and prove that for a BLD-mapping between generalized manifolds equipped with complete path-metrics, this property is equivalent to the branch set being porous when the codomain is LLC. peerReviewed