Representation Theory of Symmetric Groups and Combinatorics

Authors

  • Haoyue Jiao

DOI:

https://doi.org/10.61173/srrcfe14

Keywords:

Symmetric Groups, Standard Young Tab-leaux, SYT, Hook Length Formula, Irreducible Represen-tations, Catalan Numbers

Abstract

This paper contains an introduction of representation theory of symmetric groups and several applications in Combinatorics. By using Hook length Formula, we then consider two specific shaped Standard Young Tableaux (SYT) where (n, n) shaped SYT has a connection with Catalan Numbers and the number of ways to fill a triangular formed SYT represents the largest irreducible representation of such symmetric group.

References

dia of Integer Sequences, 2014. Published electronically at https://oeis.org/A006882. [Sta15] Richard P Stanley. Catalan numbers. Cambridge University Press, 2015.

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Published

2025-07-06

Issue

Vol. 3 No. 3 (2025): Volume 3, Issue 3

Section

Articles

License

Copyright (c) 2025 by the authors.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.