广义核划分与丢番图方程
组合数学
2025-09-23 v2 数论
表示论
摘要
我们研究由任意Dynkin型中仿射Grassmannian元素产生的广义核划分。其对应的大小概念由[CLG22]意义上的原子长度给出。在本文中，我们首先发展了扩展仿射Weyl群的理论。在一系列应用中，通过细化[BN22]和[Alp14]的结果并将其推广到更多类型，我们给出了某些类似于Pell方程的丢番图方程解的显著参数化。
引用
@article{arxiv.2403.11191,
title = {Generalised core partitions and Diophantine equations},
author = {Olivier Brunat and Nathan Chapelier-Laget and Thomas Gerber},
journal= {arXiv preprint arXiv:2403.11191},
year = {2025}
}
备注
Version 2, with some major additions and modifications: - Sections 1 and 2 revisited with important details added, - Section 3 is the fusion of previous Sections 3 and 4. Uniform proofs are provided and Theorem 3.9 is reformulated, - Section 8 is new and deals with 4-cores (10 pages), with Theorems 8.3, 8.5, 8.12 and 8.14 as new main results