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- :'''Instance''': <math>n</math> positive integers <math>x_1<x_2<\cdots <x_n</math>. ...4 KB (696 words) - 02:57, 21 October 2016
- where <math>\mathbb{N}</math> is the set of all nonnegative integers. Compared to the LP for the max-flow problem, we just replace the last line Due to the Flow Integrality Theorem, when capacities are integers, there must be an integral flow whose value is maximum among all flows (int ...21 KB (4,167 words) - 09:57, 4 January 2011
- ...s: it guarantees that the median is always a list element (e.g., a list of integers will never have a fractional median), and it guarantees that the median exi ...4 KB (751 words) - 08:12, 21 August 2016
- [[Category:Integers]] ...5 KB (804 words) - 20:06, 6 April 2017
- ...math>k</math>-compositions (the ''ordered'' sum of <math>k</math> positive integers). There are <math>{n-1\choose k-1}</math> many <math>k</math>-compositions ...integer <math>n</math>, let <math>\phi(n)</math> be the number of positive integers from <math>\{1,2,\ldots,n\}</math> that are relative prime to <math>n</math ...29 KB (5,077 words) - 04:54, 7 October 2010
- 6 KB (828 words) - 00:07, 11 November 2015
- ...and <math>N</math> be a random variable taking values in the non-negative integers and independent of the <math>X_n</math> for all <math>n \ge 1</math>. Prove ...th> uniformly at random, where <math>n</math> and <math>q</math> are given integers with <math>q \ge 1</math>. Find the expected number of inversions in <math> ...14 KB (2,403 words) - 10:41, 7 April 2023
- :'''Instance''': <math>n</math> positive integers <math>x_1<x_2<\cdots <x_n</math>. ...5 KB (877 words) - 09:10, 22 November 2017
- :Let <math>k,\ell</math> be positive integers. Then there exists an integer <math>R(k,\ell)</math> satisfying: :Let <math>r, k_1,k_2,\ldots,k_r</math> be positive integers. Then there exists an integer <math>R(r;k_1,k_2,\ldots,k_r)</math> satisfyi ...25 KB (4,530 words) - 12:14, 26 May 2023
- :Let <math>k,\ell</math> be positive integers. Then there exists an integer <math>R(k,\ell)</math> satisfying: :Let <math>r, k_1,k_2,\ldots,k_r</math> be positive integers. Then there exists an integer <math>R(r;k_1,k_2,\ldots,k_r)</math> satisfyi ...25 KB (4,530 words) - 12:14, 29 May 2024
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 07:16, 8 October 2011
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 14:54, 28 September 2017
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 06:16, 8 October 2019
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 04:35, 17 October 2016
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 14:25, 29 March 2023
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 04:27, 27 March 2024
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 03:56, 27 October 2015
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 05:36, 19 March 2014
- For any tuple <math>\mathbf{v}=(n_1,n_2,\ldots,n_m)</math> of nonnegative integers satisfying that <math>n_1+n_2+\cdots +n_m=n</math>, let <math>a_{\mathbf{v} Let <math>\mathbf{v}=(n_1,\ldots,n_m)</math> be a vector of nonnegative integers satisfying that <math>n_1+\cdots+n_m=n</math>, and let <math>a_{\mathbf{v}} ...19 KB (3,695 words) - 10:46, 17 April 2013
- ...integer <math>n</math>, let <math>\phi(n)</math> be the number of positive integers from <math>\{1,2,\ldots,n\}</math> that are relative prime to <math>n</math Let <math>U=\{1,2,\ldots,n\}</math> be the universe. The number of positive integers from <math>U</math> which is divisible by some <math>p_{i_1},p_{i_2},\ldots ...33 KB (6,205 words) - 01:11, 22 September 2011