Volker Strehl | Friedrich-Alexander-Universität Erlangen-Nürnberg (original) (raw)

Papers by Volker Strehl

Computeralgebra-Rundbrief, 2013

Mathematics Magazine, Feb 1, 1993

Computer Algebra Handbook, 2003

ABSTRACT

arXiv (Cornell University), Feb 12, 2007

We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations w... more We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigen-abelian varieties for these endomorphisms are generalizations of Prym-Tyurin varieties and naturally contain special curves representing cohomology classes which are not expected to be represented by curves in generic abelian varieties.

arXiv (Cornell University), Aug 12, 2010

In recent work on nonequilibrium statistical physics, a certain Markovian exclusion model called ... more In recent work on nonequilibrium statistical physics, a certain Markovian exclusion model called an asymmetric annihilation process was studied by Ayyer and Mallick. In it they gave a precise conjecture for the eigenvalues (along with the multiplicities) of the transition matrix. They further conjectured that to each eigenvalue, there corresponds only one eigenvector. We prove the first of these conjectures by generalizing the original Markov matrix by introducing extra parameters, explicitly calculating its eigenvalues, and showing that the new matrix reduces to the original one by a suitable specialization. In addition, we outline a derivation of the partition function in the generalized model, which also reduces to the one obtained by Ayyer and Mallick in the original model. Résumé. Dans un travail récent sur la physique statistique horséquilibre, un certain modèle d'exclusion Markovien appelé "processus d'annihilation asymétriques" aétéétudié par Ayyer et Mallick. Dans ce document, ils ont donné une conjecture précise pour les valeurs propres (avec les multiplicités) de la matrice stochastique. Ils ont en outre supposé que, pour chaque valeur propre, correspond un seul vecteur propre. Nous prouvons la première de ces conjectures en généralisant la matrice originale de Markov par l'introduction de paramètres supplémentaires, calculant explicitement ses valeurs propres, et en montrant que la nouvelle matrice se réduità l'originale par une spécialisation appropriée. En outre, nous présentons un calcul de la fonction de partition dans le modèle généralisé, ce qui réduit egalementà celle obtenue par Ayyer et Mallick dans le modèle original.

International Journal of Mathematics, 2015

Let [Formula: see text] be a smooth projective complex curve of genus [Formula: see text]. We inv... more Let [Formula: see text] be a smooth projective complex curve of genus [Formula: see text]. We investigate the Brill–Noether locus consisting of stable bundles of rank 2 and determinant [Formula: see text] of odd degree [Formula: see text] having at least [Formula: see text] independent sections. This locus possesses a virtual fundamental class. We show that in many cases this class is nonzero, which implies that the Brill–Noether locus is nonempty. For many values of [Formula: see text] and [Formula: see text] the result is best possible. We obtain more precise results for [Formula: see text]. Appendix A contains the proof of a combinatorial lemma which we need.

Dedicated to Herb Wilf on the occasion of his 80th birthday Abstract. We define a de Bruijn proce... more Dedicated to Herb Wilf on the occasion of his 80th birthday Abstract. We define a de Bruijn process with parameters n and L as a certain continuous-time Markov chain on the de Bruijn graph with words of length L over an n-letter alphabet as vertices. We determine explicitly its steady state distribution and its characteristic polynomial, which turns out to decompose into linear factors. In addition, we examine the stationary state of two specializations in detail. In the first one, the de Bruijn-Bernoulli process, this is a product measure. In the second one, the Skin-deep de Bruin process, the distribution has constant density but nontrivial correlation functions. The two point correlation function is determined using generating function techniques. 1.

Discrete Mathematics, 1992

Strehl, V., Identities of Rothes-Abel-Schläfli-Hurwitz-type, Discrete Mathematics 99 (1992) 32r-3... more Strehl, V., Identities of Rothes-Abel-Schläfli-Hurwitz-type, Discrete Mathematics 99 (1992) 32r-340. Several convolution identities, containing many free parameters, are shown to follow in a very simple way from a combinatorial construction. By specialization of the parameters one can find many of the known generalizations or variations of Abel's generalization of the binomial theorem, including those obtained by Rothe, Schläfli, and Hurwitz. A convolution identity related to Mellin's expansion of algebraic functions, proposed recently by Louck (but contained in equivalent form in earlier work by Raney and Mohanty), and a counting formula for labelled trees by rising edges, due to Kreweras, are also shown to follow from the general approach.

This thesis focuses on the practical aspects of general two-party Secure Function Evaluation (SFE... more This thesis focuses on the practical aspects of general two-party Secure Function Evaluation (SFE). A new SFE protocol that allows free evaluation of XOR gates and is provably secure against semi-honest adversaries in the random oracle model is given. Furthermore, the extension of SFE to private functions (PF-SFE) using universal circuits is considered. Based on a new practical universal circuit construction, FairplayPF is implemented that extends Fairplay, a well known SFE system, with PF-SFE.

Electronic Journal of Combinatorics, 1998

These comments contain a somewhat shorter proof of Atkinson's Theorem 2 and give some pointers to... more These comments contain a somewhat shorter proof of Atkinson's Theorem 2 and give some pointers to closely related literature. Let s_n denote the set of skew-merged permutations of [1::n]. The characteristic property of these permutations is precisely described in the title of Atkinson's article. Each such permutation, if represented as a cloud of points on a n n-grid in the traditional manner, has a number k (where 0 <= k <=n) of white elements (see Atkinson, Theorem 1). These are the elements that simultaneously belong to an increasing subsequence of maximum length and to a decreasing subsequence of maximum length. We will denote by t_k(n) the set elements of s_n with precisely k white elements (which form an increasing or decreasing sequence of contiguous elements). For further reference we introduce the set y_n: = t_1(n)+t_2(n)+:::+ t_n(n) of skew-merged permutations with at least one white element. In the sequel I use the symbols s_n, t_k(n),y_n also to denote the cardinalities...

We want to draw the combintorialists attention to an important, but apparently little known paper... more We want to draw the combintorialists attention to an important, but apparently little known paper by the function theorist A. Hurwitz, published in 1891, where he announces the solution of a counting problem which has gained some attention recently: in how many ways can a given permutation be written as the product of transpositions such that the transpositions generate the full symmetric group, and such that the number of factors is as small as possible (under this side condition). The function theoretic origin and interest of this problem will not be discussed in the present note-see the original paper by Hurwitz[14]. Current work on related problems is contained e.g. in the article by El Marraki et al. [9] in this volume.

Bayreuther Mathematische Schriften, 1992

It is shown that the method for obtaining generating functions for isomorphism types of endofunct... more It is shown that the method for obtaining generating functions for isomorphism types of endofunctions, as proposed by N.G. deBruijn and D.A. Klarner in contrast to the traditional approach of Pólya theory, can be enriched by introducing a cycle counting parameter. This parameter keeps track of the number of factors in the well-known Lyndon factorization of words. As an application, a result on isomorphism types of Jacobi configurations obtained recently by H. Décoste is reproved in this context in a completely different way.

Journal of Symbolic Computation, Nov 1, 1995

A binomial identity ((1) below), which relates the famous Apéry numbers and the sums of cubes of ... more A binomial identity ((1) below), which relates the famous Apéry numbers and the sums of cubes of binomial coefficients (for which Franel has established a recurrence relation almost 100 years ago), can be seen as a particular instance of a Legendre transform between sequences. A proof of this identity can be based on the more general fact that the Apéry and Franel recurrence relations themselves are conjugate via Legendre transform. This motivates a closer look at conjugacy of sequences satisfying linear recurrence relations with polynomial coefficients. The rôle of computer-aided proof and verification in the study of binomial identities and recurrence relations is illustrated, and potential applications of conjugacy in diophantine approximation are mentioned. This article is an expanded version of a talk given at the 29. meeting of the Séminaire Lothringien de Combinatoire, Thurnau, september 1992.