a branch of mathematics dealing with combinations and permutations
Examples of 'combinatorics' in a sentence
combinatorics
This paper deals with the problems of combinatorics optimization.
Wieslaw Wajs 1999, 'Optimistic and Pessimistic Result of Planning and Scheduling Dynamic Processes', Computer Sciencehttp://www.csci.agh.edu.pl/11/1/cs1999%2D02.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
This work uses combinatorics, graph theory, and elementary and analytical number theory.
Daniel Khoshnoudirad 2015, 'A further study for the upper bound of the cardinality of Farey vertices and applicationin discrete geometry', Journal of Algebra Combinatorics Discrete Structures and Applicationshttp://eds.yildiz.edu.tr/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=2169. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Those paradigms contribute in particular to combinatorics, formal languages and computability theories.
Vladimir Rogojin 2010, 'On computational properties of gene assembly in ciliates', Computer Science Journal of Moldovahttp://www.math.md/files/csjm/v18-n2/v18-n2-(pp171-209).pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combinatorics.
Pawel Blasiak, Gérard H. E. Duchamp, Karol A. Penson 2018, 'Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity',Advances in Mathematical Physicshttp://dx.doi.org/10.1155/2018/9575626. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Research in combinatorics on words goes back a century.
S. Vijayachitra, K. Sasikala 2016, 'Compatibility and Conjugacy on Partial Arrays', Computational and Mathematical Methods in Medicinehttp://dx.doi.org/10.1155/2016/5010316. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics.
Khodakhast Bibak, Bruce M. Kapron, Venkatesh Srinivasan 2016, 'Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclicgroup with motivations from string theory and QFT', Nuclear Physics Bhttp://www.sciencedirect.com/science/article/pii/S0550321316302115. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
However, the sleep-dependent consolidation of sentence-level combinatorics has not been studied to date.
Zachariah R. Cross, Mark J. Kohler, Mark J. Kohler, Matthias Schlesewsky, M. G. Gaskell,Ina Bornkessel-Schlesewsky 2018, 'Sleep-Dependent Memory Consolidation and Incremental Sentence Comprehension: ComputationalDependencies during Language Learning as Revealed by Neuronal Oscillations', Frontiers in Human Neurosciencehttp://journal.frontiersin.org/article/10.3389/fnhum.2018.00018/full. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
On the other hand, automata appear in various contexts in topology, combinatorics, and integrable systems.
Tsuyoshi Kato 2010, 'Geometric Representations of Interacting Maps', International Journal of Mathematics and Mathematical Scienceshttp://dx.doi.org/10.1155/2010/783738. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.
Maria Simonetta Bernabei, Horst Thaler 2010, 'Central Limit Theorem for Coloured Hard Dimers', Journal of Probability and Statisticshttp://dx.doi.org/10.1155/2010/781681. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We review some recent results in digital geometry obtained by using a combinatorics on words approach to discrete geometry.
Srečko Brlek 2011, 'Interactions between Digital Geometry and Combinatorics on Words', Electronic Proceedings in Theoretical Computer Sciencehttp://arxiv.org/pdf/1108.3615v1. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)