Enumerating Structures: Applications of the Hyperoctahedral Group in Combinatorial Species
Article Sidebar
Main Article Content
Abstract
Abstract
Combinatorial species provide a framework for counting and classifying for counting and classifying combinatorial structures. A species assigns a set of structures to each finite set, respecting the notion of isomorphism. This approach facilitates the enumeration of various combinatorial objects. The hyperoctahedral group, also known as the signed permutation group, consists of permutations of a set of signed elements. This group plays a crucial role in combinatorial algebra, particularly in the enumeration of certain structures, such as various types of trees and graphs. Generating series, both ordinary and exponential, are powerful tools in combinatorial enumeration. Combining these concepts allows for deeper insights into the relationships between structures and their enumerative properties, paving the way for advanced combinatorial theory and applications in various mathematical fields.
Downloads
Article Details
Copyright (c) 2024 Gabriel Cedric PB.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensing and protecting the author rights is the central aim and core of the publishing business. Peertechz dedicates itself in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. Peertechz licensing terms are formulated to facilitate reuse of the manuscripts published in journals to take maximum advantage of Open Access publication and for the purpose of disseminating knowledge.
We support 'libre' open access, which defines Open Access in true terms as free of charge online access along with usage rights. The usage rights are granted through the use of specific Creative Commons license.
Peertechz accomplice with- [CC BY 4.0]
Explanation
'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.
Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific license.
With this license, the authors are allowed that after publishing with Peertechz, they can share their research by posting a free draft copy of their article to any repository or website.
'CC BY' license observance:
|
License Name |
Permission to read and download |
Permission to display in a repository |
Permission to translate |
Commercial uses of manuscript |
|
CC BY 4.0 |
Yes |
Yes |
Yes |
Yes |
The authors please note that Creative Commons license is focused on making creative works available for discovery and reuse. Creative Commons licenses provide an alternative to standard copyrights, allowing authors to specify ways that their works can be used without having to grant permission for each individual request. Others who want to reserve all of their rights under copyright law should not use CC licenses.
Labelle J, Yeh Y. The relation between Burnside rings and combinatorial species. Journal of Combinatorial Theory. 1989;269-284. Available from: https://doi.org/10.1016/0097-3165(89)90019-8
Cedric P.B.G., Ndoumbe Moïse I. The transport of species of structures along the braid group. Journal of Physical Mathematics and its Applications. SRC/JPMA-134. 2024. Available from: http://dx.doi.org/10.47363/JPMA/2024(2)117
Cedric P.B.G., Ndoumbè Moïse I. The symmetry of enumerative combinatorial structures. 2024;hal-04674689. Available from: https://hal.science/hal-04674689v1/document
Mbiang B. The use of generating series in enumerative combinatorics. Master’s thesis, University of Douala, 2012-2013.
Nunge A. An equivalence of multistatistics on permutations. Journal of Combinatorial Theory, Series A. 2018;157:435-460. Available from: https://doi.org/10.1016/j.jcta.2018.03.005
Porier S. Symmetric functions, descent sets, and conjugacy classes in wreath products. Ph.D. thesis, Université du Québec à Montréal, Canada.1995.
Joyal A. A combinatorial theory of formal series. Advances in Mathematics. 1982;42:1-82. Available from: https://doi.org/10.1016/0001-8708(81)90052-9
Décoste H. Introduction to the theory of species. Course notes, Concordia University, Montréal, Canada. 1986.
Rougé A. Introduction to subatomic physics. Les Editions de l'Ecole Polytechnique, Palaiseau, France. 2005.
Rossmann W. Lie groups: An introduction through linear groups. Oxford University Press, Oxford, UK. 2002.