The transport of combinatorial structures via braid group actions : A species-theoretic approach
Pemha Binyam Gabriel Cedricgpemha@yahoo.frDepartment of Mathematics and Computer SciencesFaculty of SciencesUniversity of DoualaDouala, PO. Box 24157, Cameroon0009-0004-9987-8696View full profile →
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- Received:
- 01 Aug 2025
- Published Online:
- 29 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-2200
- Pages:
- 1–10
Abstract
This paper introduces a novel framework for the transport of combinatorial structures using the braid group Bm, generalizing the classical theory of species of structures developed by Joyal and Bergeron. While traditional species theory relies on symmetric group actions for label permutations, our approach leverages the richer algebraic structure of braid groups to encode topological and combinatorial relabelings of t-structures-objects constructed over finite sets with m-strand elements. We define t-structures as pairs (γt, [U]m), where γt is a construction on [U]m, and establish their transport along braid group bijections ωt : [U]m→[V]m as functorial operations. Key contributions include:
• A rigorous formulation of braid group actions on species of t-structures, with explicit examples (e.g. rooted trees).
• Proofs of isomorphism invariance under transport, demonstrating that t-structures preserve their combinatorial type under relabeling by braid words.
• Connections to geometric braid diagrams and algebraic presentations of Bm, highlighting the interplay between combinatorics and low-dimensional topology.
Our results extend the scope of enumerative combinatorics by incorporating braidtheoretic symmetries, paving the way for future work on generating series and cycle index techniques for t-structures. This work bridges gaps between species theory, braid groups, and labeled/unlabeled enumeration, offering tools for recursive structural analysis in mathematics and theoretical computer science.
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References
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