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Combinatorially Meaning: Definition, Examples, and Translations

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combinatorially

[kəmˈbɪnəˈtɔːrɪəli ]

Definitions

Context #1 | Adverb

in mathematics

In a combinatorial manner; in relation to combinations of items rather than permutations.

Examples of usage

  • Combinatorially, the number of ways to choose 2 items from a set of 4 is 6.
  • The problem can be solved combinatorially by using the binomial coefficient formula.
Context #2 | Adverb

in computer science

In a manner related to the branch of mathematics dealing with combinations, permutations, and arrangements.

Examples of usage

  • The algorithm works combinatorially to generate all possible combinations of the input data.
  • Combinatorially speaking, the complexity of the problem increases exponentially with the size of the input.

Translations

To see the translation, please select a language from the options available.

Interesting Facts

Mathematics

  • In combinatorial mathematics, the focus is on counting, arrangement, and grouping of objects based on defined rules.
  • Permutations and combinations are two fundamental concepts, where permutations involve arrangements, while combinations are selections without arrangement.
  • The famous 'Pigeonhole Principle' states that if you have more items than containers, at least one container must hold more than one item, demonstrating a basic combinatorial concept.

Computer Science

  • Combinatorial algorithms are essential in computer science for solving problems like sorting, searching, and optimizing network traffic.
  • The concept is widely used in cryptography, where secure codes often rely on combinatorial principles to generate keys.
  • Mathematical models based on combinatorics help analyze data structures like graphs, which are crucial for network operations.

Game Theory

  • Many problems in game theory are analyzed combinatorially, exploring strategies and possible outcomes based on players' choices.
  • Concepts such as Nash Equilibrium can involve combinatorial considerations when determining optimal strategies in competitive scenarios.
  • The combinatorial nature of games often leads to intricate analysis of moves and counter-moves, creating complex decision trees.

Biology

  • In genetics, combinatorial principles explain how different traits combine during reproduction, affecting the variation seen in populations.
  • The structure of DNA and how genes combine can be studied through combinatorial approaches, providing insights into heredity.
  • The formation of protein structures often involves combinatorial arrangements of amino acids, crucial for understanding biological functions.

Origin of 'combinatorially'

Main points about word origin

  • The term comes from 'combination', which has roots in the Latin 'combinare', meaning 'to put together'.
  • The suffix '-ally' in English is used to form adverbials, signaling a manner or way of doing something.
  • The concept of combinatorial mathematics emerged in the 17th century, as mathematicians began exploring arrangements and selections.

The word 'combinatorially' is derived from the word 'combinatorial,' which comes from the Latin word 'combinare,' meaning 'to combine.' The concept of combinatorics has a long history, with roots in ancient civilizations like China and India. It became a formal branch of mathematics in the 17th century and has since been applied in various fields such as mathematics, computer science, and statistics.

Word Frequency Rank

At position #40,538, this word is among the less frequently used terms in English. While interesting to know, it's not crucial for most English learners unless needed for specific purposes.