# Book for matroid polytopes

I have made a study of polytopes with the books of Ziegler and "Integer Programming" of Conforti, my main goal is to study matroid polytopes; to study matroids I have thought about the book "MATROID THEORY" of Welsh. But how do I connect the two topics, i.e. polytopes with matroids? I am not clear if in the same text of Welsh this is specified, or if there is any additional reference to do this work? Any suggestions are welcome!

• I don't think there is a book on matroid polytopes. And learning about matroids in general, like from the textbook of Welsh, is a good idea, but I'm not sure it will help you understand contemporary research in matroid polytopes. I might suggest you learn about generalized permutohedra (alias polymatroids), a slightly larger class of polytopes that includes matroid polytopes. The classic papers here are "Permutohedra, associahedra, and beyond" by Postnikov arxiv.org/abs/math/0507163 and "Faces of Generalized Permutohedra" by Postinkov-Reiner-Williams arxiv.org/abs/math/0609184. Dec 12, 2023 at 16:18
• Sounds nice! Please write down the stuff you learn and share! Dec 12, 2023 at 19:08
• @SamHopkins Do you think that studying the type of matroids that you indicate can be used to write a monograph, which is the final work for undergraduate studies in mathematics? I say this because it can be a topic that, in depth, can be something that exhibits a section interesting of the polytopes, or on the contrary, do you think that related to this there is some result/theorem/example that is more interesting?. Your recommendation is very useful! I appreciate it; Dec 13, 2023 at 2:38
• I don't quite understand your last question, but if you're asking if matroid polytopes would be a reasonable topic for an undergraduate thesis, then I would say yes. And in fact, a quick search on Google lead me to this bachelor thesis on matroid polytopes by Christoph Pegel, which you might be interested in: iazd.uni-hannover.de/fileadmin/iazd/Pegel/… Dec 13, 2023 at 2:40
• @SamHopkins Exactly, my question is what you mention; Furthermore, I was wondering if I could lead the thesis towards Postnikov's article with the article "Faces of Generalized Permutohedra", studying this article in depth would be a good approach? I appreciate your comments from your experience. pd:The last article you attached looks really interesting, thank you so much for it! Dec 13, 2023 at 2:44