Editing Combinatorics (section)

{{Short description|Branch of discrete mathematics}}
{{Distinguish|Combinatoriality}}
{{Redirect | Combinatorial | combinatorial logic in computer science | Combinatorial logic }}
{{More footnotes needed|date=July 2022}}
{{Math topics TOC|expanded=Pure mathematics}}
'''Combinatorics''' is an area of [[mathematics]] primarily concerned with [[counting]], both as a means and as an end to obtaining results, and certain properties of [[finite set|finite]] [[Mathematical structure|structures]]. It is closely related to many other areas of mathematics and has many applications ranging from [[logic]] to [[statistical physics]] and from [[evolutionary biology]] to [[computer science]].

Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of [[pure mathematics]], notably in [[algebra]], [[probability theory]], [[topology]], and [[geometry]],<ref>Björner and Stanley, p. 2</ref> as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right.<ref>{{cite book|last1=Lovász|first1=László|title=Combinatorial Problems and Exercises|date=1979|publisher=North-Holland|quote=In my opinion, combinatorics is now growing out of this early stage.|url=https://books.google.com/books?id=ueq1CwAAQBAJ&pg=PP1|isbn=978-0821842621|access-date=2021-03-23|archive-date=2021-04-16|archive-url=https://web.archive.org/web/20210416100842/https://books.google.com/books?id=ueq1CwAAQBAJ&pg=PP1|url-status=live}}</ref> One of the oldest and most accessible parts of combinatorics is [[graph theory]], which by itself has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the [[analysis of algorithms]].