II. Institut für Mathematik, Freie Universität Berlin, Königin-Luise-Strasse 24/26, 1000, Berlin 33, Federal Republic of Germany
II. Institut für Mathematik, Freie Universität Berlin, Königin-Luise-Strasse 24/26, 1000, Berlin 33, Federal Republic of Germany
variety
finite posets
unrelated methods
authors
combinatorics
existence results
difficulties
aspects
matroids
1979
apparent difficulty
combinatorial theory
https://doi.org/10.1007/978-1-4615-6666-3
computer
monograph
differences
field
1979-01-01
Hall
vast variety
function
design
respect
calculus
old books
past year
consensus
en
lattice
science
978-1-4615-6666-3
method
inversion
present book
most authors
permutation groups
group
large part
finite differences
mathematics
978-1-4615-6668-7
one
results
point
book
2022-05-10T10:34
posets
enumeration
It is now generally recognized that the field of combinatorics has, over the past years, evolved into a fully-fledged branch of discrete mathematics whose potential with respect to computers and the natural sciences is only beginning to be realized. Still, two points seem to bother most authors: The apparent difficulty in defining the scope of combinatorics and the fact that combinatorics seems to consist of a vast variety of more or less unrelated methods and results. As to the scope of the field, there appears to be a growing consensus that combinatorics should be divided into three large parts: (a) Enumeration, including generating functions, inversion, and calculus of finite differences; (b) Order Theory, including finite posets and lattices, matroids, and existence results such as Hall's and Ramsey's; (c) Configurations, including designs, permutation groups, and coding theory. The present book covers most aspects of parts (a) and (b), but none of (c). The reasons for excluding (c) were twofold. First, there exist several older books on the subject, such as Ryser [1] (which I still think is the most seductive introduction to combinatorics), Hall [2], and more recent ones such as Cameron-Van Lint [1] on groups and designs, and Blake-Mullin [1] on coding theory, whereas no compre hensive book exists on (a) and (b).
order theory
Combinatorial Theory
discrete mathematics
lint
years
theory
subjects
Ramsey
configuration
part
branches
reasons
books
Ryser
scope
most aspects
false
field of combinatorics
https://scigraph.springernature.com/explorer/license/
natural sciences
fact
recent ones
pub.1011173064
dimensions_id
Mathematical Sciences
Aigner
Martin
Springer Nature - SN SciGraph project
Pure Mathematics
doi
10.1007/978-1-4615-6666-3
Springer Nature