CEU Electronic Theses and Dissertations, 2020
| Author | Madireddi, Sai Praveen |
|---|---|
| Title | An Insight into Foulkes Conjecture |
| Summary | Foulkes module $F_{a}^{b}$ is the permutation module of the set of partition of $ab$ elements into size $a$ each. $F_{a}^{b}$ $\cong$ $1_{S_a wr S_b} \uparrow^{S_{ab}}$. The study goes back to 1942, when Thrall computed the structure of $F_{2}^{b}$ and $F_{b}^{2}$. In 1950, Foulkes while analysing the structure of $F_{m}^{n}$ for some specific $m$ and $n$ observed that $F_{n}^{m}$ can be embedded in $F_{m}^{n}$ when $m < n$ and thus conjectured that if $a < b$, $F_{b}^{a}$ can be embedded in $F_{a}^{b}$. I will describe the progress on Foulkes conjecture and briefly explain the methods used by Tom Mckay and Eugenio Giannelli to prove their results. I will also explain the structure of $F_{a}^{b} \downarrow_{S_K \times S_{ab -k}}$ as a direct sum of permutation modules and study the structure of such permutation modules. |
| Supervisor | Hegedüs, Pál |
| Department | Mathematics Ps |
| Full text | https://www.etd.ceu.edu/2020/madireddi_sai.pdf |
Visit the CEU Library.
© 2007-2021, Central European University