R&E 21
Catalogue of all Book Series
List of Books in this Series
Previous Book
Next Book


Research and Exposition in Mathematics  Volume 21
Enlarged Picture
K. Denecke, O. Lüders (eds.)
General Algebra and Discrete Mathematics
272 p., soft cover, ISBN 3885382210, 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 nondiscrete 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.
Contents
Preface, 12
 R. Bodendiek, G. Walter
 On Number Theoretical Methods in Graph Labellings
326
A. Bulatov, A. Krokhin, K. Safin, E. Sukhanov
 On the Structure of Clone Lattices,
2734
I. Chajda
 Congruence Properties of Algebras in Nilpotent Shifts of Varieties,
3546
S. Dahlke
 The Construction of Wavelets on Groups and Manifolds,
4758
K. Denecke, D. Lau, R. Poeschel, D. Schweigert
 Free Clones and Solid Varieties,
5982
K. Denecke, J. Plonka
 Regularization and Normalization of Solid Varieties,
8392
D. Dimovski
 On (m+k, m)  Groups for k < m,
93100
J. Duda
 dfold Projections of Subalgebras, Homomorphisms, and Congruence Classes,
101106
K. GajewskaKurdziel
 On the Lattice of some Varieties Defined by Externally Compatible Identities,
107110
E. Graczynska
 Regular Identities H,
111130
K. Halkowska
 Free Algebras over PCompatible Varieties,
131136
H.J. Hoehnke
 On Certain Classes of Categories and Monoids Constructed from Abstract Mal'cev Clones, IV,
137168
I. Korec
 Decidable and Undecidable Theories of Generalized Pascal Triangles,
169180
V. Levignon, S. E. Schmidt
 A Geometric Approach to Generalized Matroid Lattices,
181186
O. M. Mamedov
 On the Lattice of Interpretability Types of Varieties,
187190
I. Mirchev
 Separable and Dominating Sets of Variables for Functions,
191198
J. Plonka
 On Hyperidentities of some Varieties,
199214
M. Reichel
 Free Spectra and Hyperidentities,
215226
H.J. Vogel
 On Quasivarieties Generated by DiagonalInversionAlgebras,
227242
W. Wessel
 Are All Complete Plane Multimaps But One Bounded by Euler Only?,
243272
