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Research and Exposition in Mathematics -- Volume 21

   Enlarged Picture

K. Denecke, O. Lüders (eds.)

General Algebra and Discrete Mathematics

272 p., soft cover, ISBN 3-88538-221-0, EUR 38.00, 1995

This volume contains articles based on lectures given at the "Fourth Conference on Discrete Mathematics", which took place at Potsdam in 1993.
The articles put in evidence some aspects of the natural interaction between General Algebra and Discrete Mathematics.
Algebraic structures such as semigroups, lattices, Boolean algebras, function algebras, and relation algebras, or ordered algebraic structures, form a structural background of such fields of Discrete Mathematics as formal languages, the theory of automata, theoretical computer science, and graph theory.
The distinction between discrete and non-discrete mathematics has perhaps something to do with the distinction between analog computers and digital computers. At any rate, the beginning of Discrete Mathematics as an own branch of mathematics is connected with the development of digital computers. Roughly, this distinction is analogous to the distinction between measuring and counting.
But all analog computers made by man have one serious defect; they do not measure accurately enough. The difficulty comes from the fact that the device records the continuous changes continuously. As a result there is always a very small ambiguity in its readings. A digital computer has no such defect. It is a machine to calculate numbers, not measuring phenomena. An analog signal has continuously valid interpretations. A digital signal has only a discrete number of valid interpretations, often a finite number. The digital signal is therefore always clear, never ambiguous; as a result calculations can be arranged to deliver exactly correct results. A finitary operation defined on a finite set models a digital device with a finite number of inputs and one output where a signal has only interpretations in this finite set. This model is one of the basic ingrediences of the papers presented in this volume.


Preface, 1--2

R. Bodendiek, G. Walter
On Number Theoretical Methods in Graph Labellings

A. Bulatov, A. Krokhin, K. Safin, E. Sukhanov
On the Structure of Clone Lattices,

I. Chajda
Congruence Properties of Algebras in Nilpotent Shifts of Varieties,

S. Dahlke
The Construction of Wavelets on Groups and Manifolds,

K. Denecke, D. Lau, R. Poeschel, D. Schweigert
Free Clones and Solid Varieties,

K. Denecke, J. Plonka
Regularization and Normalization of Solid Varieties,

D. Dimovski
On (m+k, m) - Groups for k < m,

J. Duda
d-fold Projections of Subalgebras, Homomorphisms, and Congruence Classes,

K. Gajewska-Kurdziel
On the Lattice of some Varieties Defined by Externally Compatible Identities,

E. Graczynska
Regular Identities H,

K. Halkowska
Free Algebras over P-Compatible Varieties,

H.-J. Hoehnke
On Certain Classes of Categories and Monoids Constructed from Abstract Mal'cev Clones, IV,

I. Korec
Decidable and Undecidable Theories of Generalized Pascal Triangles,

V. Levignon, S. E. Schmidt
A Geometric Approach to Generalized Matroid Lattices,

O. M. Mamedov
On the Lattice of Interpretability Types of Varieties,

I. Mirchev
Separable and Dominating Sets of Variables for Functions,

J. Plonka
On Hyperidentities of some Varieties,

M. Reichel
Free Spectra and Hyperidentities,

H.-J. Vogel
On Quasivarieties Generated by Diagonal-Inversion-Algebras,

W. Wessel
Are All Complete Plane Multimaps But One Bounded by Euler Only?,