A free, non-profit, educational site for enthusiast and professional mathematicians, physicists and computer scientists.
Are you enjoying Bookof Proofs
Help us to improve the site!
We welcome any feedback, praise and criticism!
You are now going to submit your contribution for review.
You won't be able to edit it until it gets reviewed. However, you will be able to withdraw the contribution and continue editing.
You might submit an optional message for the reviewer of your contribution.
Do you want to continue?
Your contribution has been successfully withdrawn.
You are going to withdraw your contribution.
Do you want to continue?
Your vote to this contribution has been stored.
Definition: Binomial Coefficients edit contribute as guest [id:993] Notation
show notation Notation Term LateX Code \(\binom nk\) Binomial Coefficients \(\binom nk\) binomial coefficient Binomial Coefficients binomial coefficient
Let \(X\) be a finite set with exactly \(n\) elements \((|X|=n)\) and let \(X_1, \ldots, X_{t_{nk}} \) be its subsets with exactly \(k\) elements \((|X_i|=k,\forall i=1,\ldots,t_{nk})\). Then we call the number \(t_{nk}\) of such subsets the binomial coefficient and denoted it by
References
[977] Aigner, Martin: “Diskrete Mathematik”, vieweg studium, 1993
Global predecessors:
Anything in here will be replaced on browsers that support the canvas element
708: alphabet, letter, concatenation, string, empty string, formal language 668: axiom of associativity 669: axiom of existence of an identity 571: binary relations 748: cartesian product 836: groupoid (magma) 661: identity, neutral element, left identity, right identity 575: irreflexive, asymmetric and antisymmetric relation 705: law of excluded middle 659: monoid 714: negation 697: order relation for natural numbers 747: ordered pair, n-tuple 723: ordinal number 504: peano axioms 576: preorder (quasiorder), partial and total order, poset and chain 1308: properties of binary relations between two sets 721: properties of transitive sets 572: reflexive, symmetric and transitive relation 710: sematics, proposition 660: semigroup 707: set of binary logical values (true and false) 664: set of natural numbers (peano) 550: set, set element, empty set 718: set-theoretic definitions of natural numbers 552: subset, superset, union, intersection, set difference, set complement, power set 774: successor of oridinal 744: the proving principle by contradiction 592: total maps (../../branches/functions.jpg) 720: transitive set 698: well-ordering principle 1427: zermelo-fraenkel axioms
The immidiate logical predecessors and successors of the current node are: Your browser does not support SVG
Found a mistake? Fix it by editing the definition above! Learn more about the axiomatic method.
Subordinated Structure:
Contribute to Bo P
add a new Motivation add contribute as guest
add a new Example add contribute as guest
add a new Application add contribute as guest
add a new Explanation add contribute as guest
add a new Interpretation add contribute as guest
add a new Proposition add contribute as guest
add a new Lemma add contribute as guest
add a new Theorem add contribute as guest
add a new Corollary add contribute as guest
add a new Algorithm add contribute as guest
add a new Definition add contribute as guest
add a new Bibliography (Branch) add contribute as guest
add a new Comment (Branch) add contribute as guest
Warning: This site requires JavaScript to process the mathematics on this page.
