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combinatorial    
组合的

组合的

combinatorial
adj 1: relating to or involving combinations [synonym:
{combinative}, {combinatory}, {combinatorial}]
2: relating to the combination and arrangement of elements in
sets


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  • What is combinatorics? - Mathematics Stack Exchange
    Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and
  • Book on combinatorial identities - Mathematics Stack Exchange
    The book Combinatorial Identities from John Riordan ($1968$) is a wonderful classic with thousands of binomial identities which are systematically organised But it does not typically provide combinatorial proofs It's a great reference to search for different classes of combinatorial identities
  • combinatorics - What is a combinatorial proof exactly? - Mathematics . . .
    The other answers also talk about other ways to prove using Combinatorial Arguments Combinatorics is a wide branch in Math, and a proof based on Combinatorial arguments can use many various tools, such as Bijection, Double Counting, Block Walking, et cetera, so a combinatorial proof may involve any (or a combination) of these $\endgroup$
  • combinatorics - How are combinatorial classes and combinatorial species . . .
    Combinatorial classes are for unlabeled objects, while combinatorial species are for labeled objects The two methods are not analogous You say that "classes" are associated with EGF's, and I object to that phrasing because it is unclear Normally, combinatorial classes are naturally associated with OGF's
  • combinatorics - Combinatorial proof of $\sum_{k=1}^n k k!=(n+1)!-1 . . .
    Combinatorial Proof regarding Falling Factorials and sums of Falling Factorials Hot Network Questions Minimum level of superhuman ability needed for a medieval civilization to ward off USA-level foes through fear of conflict
  • Newest combinatorial-proofs Questions - Mathematics Stack Exchange
    Combinatorial proofs of identities use double counting and combinatorial characterizations of binomial
  • combinatorics - Combinatorial proof of a Stirling number identity . . .
    These are not combinatorial interpretations, but they are simple The defining equation for Stirling numbers of the second kind is $$ \sum_{k=0}^n\begin{Bmatrix}n\\k\end{Bmatrix}\binom{x}{k}k!=x^n\tag{1} $$ That is, Stirling numbers of the second kind tell how to write monomials as a combination of falling factorials (or combinatorial polynomials)
  • Books in Combinatorial optimization - Mathematics Stack Exchange
    I believe combinatorial optimization is the natural way to go from Hall and König Extremal graph theory mostly restricts itself to graphs (rather than decorated graphs, matroids, jump systems and all the other fancy objects combinatorial optimization is occupied with), about which it asks deeper questions
  • combinatorics - A comprehensive list of binomial identities . . .
    In general, Gould's work is a great resource for this sort of thing; he has spent much of his career collecting and proving combinatorial identities Added: Another useful reference is John Riordan's Combinatorial Identities It's hard to pick one of its 250 pages at random and not find at least one binomial coefficient identity there





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