Search results

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

...input a set <math>S</math> of <math>n</math> numbers, we want to sort the numbers in <math>S</math> in increasing order. One of the most famous algorithm for ...re all numbers in <math>S_1</math> are smaller than <math>x</math> and all numbers in <math>S_2</math> are larger than <math>x</math>; ...

...v</sub> || E 2C₄ C₂ 2σ_v 2σ_d || square pyramidal || [[xenon oxytetrafluoride]] ...ub>'' ''i'' 2S₄ σ_h 2σ_v 2σ_d || square planar || [[xenon tetrafluoride]] ...

If there exists a '''[[square matrix]]''' called '''''A''''', a '''[[scalar]] ''λ''''', and a '''non-zero ...cation. For example, instead of [[real numbers]], scalars may be [[complex numbers]]; instead of arrows, vectors may be [[function (mathematics)|functions]] ...

Sampling <math>t</math> mutually independent random numbers from <math>[p]</math> can be quite expensive since it requires <math>\Omega The error is reduced to <math>1/t</math> with only two random numbers. This scheme works as long as <math>t\le p</math>. ...

Sampling <math>t</math> mutually independent random numbers from <math>[p]</math> can be quite expensive since it requires <math>\Omega The error is reduced to <math>1/t</math> with only two random numbers. This scheme works as long as <math>t\le p</math>. ...

...ximation ratio of 2 to being 2-universal. The proof uses the fact that odd numbers are relative prime to a power of 2. We exploit that C-multiplication (*) of unsigned u-bit numbers is done <math>\bmod 2^u</math>, and have a one-line C-code for computing th ...

...ximation ratio of 2 to being 2-universal. The proof uses the fact that odd numbers are relative prime to a power of 2. We exploit that C-multiplication (*) of unsigned u-bit numbers is done <math>\bmod 2^u</math>, and have a one-line C-code for computing th ...

Sampling <math>t</math> mutually independent random numbers from <math>[p]</math> can be quite expensive since it requires <math>\Omega The error is reduced to <math>1/t</math> with only two random numbers. This scheme works as long as <math>t\le p</math>. ...

<math>\square</math> ...to introduce the concepts of the <math>k</math>-cascade representation of numbers and the colex order of sets. ...

<math>\square</math> ...to introduce the concepts of the <math>k</math>-cascade representation of numbers and the colex order of sets. ...

...ted as a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named afte |align=center|Ferrers diagram (''square version'') of (5,4,2,1) ...

...re related. For a vector '''a''', the dot product '''a''' · '''a''' is the square of the length of '''a''', or Unlike multiplication of ordinary numbers, where if ''ab'' = ''ac'', then ''b'' always equals ''c'' unless ''a'' is z ...

...ximation ratio of 2 to being 2-universal. The proof uses the fact that odd numbers are relative prime to a power of 2. We exploit that C-multiplication (*) of unsigned u-bit numbers is done <math>\bmod 2^u</math>, and have a one-line C-code for computing th ...