Search results for "Graph theory"

Counting degree sequences of spanning trees in bipartite graphs: A graph‐theoretic proof

2019

Groups whose real irreducible characters have degrees coprime to p

2012

Abstract In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p .

Nearly tight bounds on the learnability of evolution

2002

Evolution is often modeled as a stochastic process which modifies DNA. One of the most popular and successful such processes are the Cavender-Farris (CF) trees, which are represented as edge weighted trees. The Phylogeny Construction Problem is that of, given /spl kappa/ samples drawn from a CF tree, output a CF tree which is close to the original. Each CF tree naturally defines a random variable, and the gold standard for reconstructing such trees is the maximum likelihood estimator of this variable. This approach is notoriously computationally expensive. We show that a very simple algorithm, which is a variant on one of the most popular algorithms used by practitioners, converges on the t…

Games without repetitions on graphs with vertex disjoint cycles

1997

Games without repetitions on graphs with vertex disjoint cycles are considered. We show that the problem finding of the game partition in this class reduces to this problem for trees. A method of finding of the game partition for trees have been given in [2].

A graph associated with the $\pi$-character degrees of a group

2003

Let G be a group and $\pi$ be a set of primes. We consider the set ${\rm cd}^{\pi}(G)$ of character degrees of G that are divisible only by primes in $\pi$. In particular, we define $\Gamma^{\pi}(G)$ to be the graph whose vertex set is the set of primes dividing degrees in ${\rm cd}^{\pi}(G)$. There is an edge between p and q if pq divides a degree $a \in {\rm cd}^{\pi}(G)$. We show that if G is $\pi$-solvable, then $\Gamma^{\pi}(G)$ has at most two connected components.

The number of lifts of a Brauer character with a normal vertex

2011

AbstractIn this paper we examine the behavior of lifts of Brauer characters in p-solvable groups. In the main result, we show that if φ∈IBr(G) has a normal vertex Q and either p is odd or Q is abelian, then the number of lifts of φ is at most |Q:Q′|. As a corollary, we prove that if φ∈IBr(G) has an abelian vertex subgroup Q, then the number of lifts of φ in Irr(G) is at most |Q|.

SELF-ENERGIES AND VERTEX CORRECTIONS WITH TWO FACTORIZING LOOPS

1999

A complete set of factorizing two-loop self-energies and vertex corrections is calculated analytically for arbitrary masses and momenta — including the case of collinear singularities — within the ℛ-functions approach.

The exact bounds for the degree of commutativity of a p-group of maximal class, I

2002

Abstract The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant of these groups is the ‘degree of commutativity.’ Recently (1995) Fernandez-Alcober proved a best possible inequality for the degree of commutativity in terms of the order of the group. Recent computations for primes up to 43 show that sharper results can be obtained when an additional invariant is considered. A series of conjectures about this for all primes have been recorded in [A. Vera-Lopez et al., preprint]. In this paper, we prove two of these conjectures.

Error Bounds for the Numerical Evaluation of Integrals with Weights

1988

This paper is concerned with a procedure of obtaining error bounds for numerically evaluated integrals with weights. If \( - \infty \mathop < \limits_ = a < b\mathop < \limits_ = \infty \), w integrable over [a,b] and positive almost everywhere, then an approximation of \({I_W}f: = \int\limits_a^b {w\left( t \right)f\left( t \right)dt} \) by a quadrature rule \({Q_n}f: = \sum\limits_{i = 0}^n {{\alpha _i}f\left( {{t_i}} \right)} \) is leading to the error Enf ≔ Iwf ‒ Qnf. An algorithm is derived for the computation of bounds for |Enf| depending on the smoothness of the integrand f and on the degree of exactness of Q. As initial values this algorithm needs moments of the weighting function w…

The spatial pattern of a forest ecosystem

1998

Abstract Statistical analysis of stands of trees as a whole need suitable methods of spatial statistics. Obviously, trees within a stand affect development and survival of their neighbours. They interact and therefore have to be considered as a system of dependent random variates from an unknown stochastic process. One such statistical model which considers the spatial dependence among trees in a forest and their characteristics is a marked point process. The `points', called events in spatial statistics, are the tree positions and the `marks' are tree characteristics such as crown lengths or tree species. A minimal prerequisite for any serious attempt to model an observed pattern is to tes…