On the Number of Disconnected Character Degree Graphs Satisfying Pálfy's Inequality
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917973769322496 |
|---|---|
| author | Lewis, Mark L. Summers, Andrew |
| author_facet | Lewis, Mark L. Summers, Andrew |
| contents | Let $G$ be a finite solvable group with disconnected character degree graph $Δ(G)$. Under these conditions, it follows from a result of Pálfy that $Δ(G)$ consists of two connected components. Another result of Pálfy's gives an inequality relating the sizes of these two connected components. In this paper, we calculate the number of possible component size pairs that satisfy Pálfy's inequality. Additionally, for a fixed positive integer $n$, the number of distinct graph orders for which exactly $n$ component size pairs satisfy Pálfy's inequality is shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Number of Disconnected Character Degree Graphs Satisfying Pálfy's Inequality Lewis, Mark L. Summers, Andrew Combinatorics Group Theory 20C15 (Primary), 05C25 (Secondary) Let $G$ be a finite solvable group with disconnected character degree graph $Δ(G)$. Under these conditions, it follows from a result of Pálfy that $Δ(G)$ consists of two connected components. Another result of Pálfy's gives an inequality relating the sizes of these two connected components. In this paper, we calculate the number of possible component size pairs that satisfy Pálfy's inequality. Additionally, for a fixed positive integer $n$, the number of distinct graph orders for which exactly $n$ component size pairs satisfy Pálfy's inequality is shown. |
| title | On the Number of Disconnected Character Degree Graphs Satisfying Pálfy's Inequality |
| topic | Combinatorics Group Theory 20C15 (Primary), 05C25 (Secondary) |
| url | https://arxiv.org/abs/2504.01158 |