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Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can Let <math>A</math> be the largest independent set in <math>G</math> and let <math>\alpha=|A|</math>. ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can Let <math>A</math> be the largest independent set in <math>G</math> and let <math>\alpha=|A|</math>. ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can Let <math>A</math> be the largest independent set in <math>G</math> and let <math>\alpha=|A|</math>. ...

The basic theory, widely agreed, is that highly conserved DNA sequences must have functional ...ved DNA sequences, consist of repeated sequence elements. If only one of a set of a repeated sequences was removed, and the repetitions were not needed, t ...

Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

Let <math>A_1,A_2,\ldots,A_n\subseteq U</math> be subsets of some finite set <math>U</math>. Here <math>U</math> is some universe of combinatorial objec ...ber of surjective mappings from an <math>n</math>-set to an <math>m</math>-set is given by ...

...he problem and an output is called a '''solution''' to that instance. The theory of complexity deals almost exclusively with [http://en.wikipedia.org/wiki/D ...h "yes" answers. A decision problem can be equivalently represented as the set of all positive instances, denoted <math>L</math>. We call <math>L</math> a ...

...egral]] taken over a [[surface]] (which may be a curve [[Set (mathematics)|set]] in [[Space (physics)|space]]). Just as a [[line integral]] handles one di ...egrals have applications in [[physics]], particularly with the [[classical theory]] of [[electromagnetism]]. ...

...(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an independent set for edges, that is, for any <math>e_1,e_2\in M</math> that <math>e_1\neq e_ ...override the notation as <math>N(S)=\bigcup_{v\in S}N(v)</math>, i.e. the set of vertices that are adjacent to one of the vertices in <math>S</math>. ...

...(V,E)</math>, a '''matching''' <math>M\subseteq E</math> is an independent set for edges, that is, for any <math>e_1,e_2\in M</math> that <math>e_1\neq e_ ...override the notation as <math>N(S)=\bigcup_{v\in S}N(v)</math>, i.e. the set of vertices that are adjacent to one of the vertices in <math>S</math>. ...

...n of compounds with more than two functional groups. He also developed the theory of polymer networks or [[gels]]. ...Development Company.<ref name=nb1 /> He developed a statistical mechanical theory for polymer mixtures there. ...

== Principles in probability theory == * '''Basics of probability theory''': probability space, events, the union bound, independence, conditional p ...

== Principles in probability theory == * '''Basics of probability theory''': probability space, events, the union bound, independence, conditional p ...

...t system is a '''sunflower''' if all its member sets intersect at the same set of elements. : A set family <math>\mathcal{F}\subseteq 2^X</math> is a '''sunflower''' of size < ...