What Are Some Resources for Learning About Lattice Theory Coloring?

[iamalexalright]

I don't know if this is the proper place but I'll put it here.

I just started doing my OURE on lattice coloring. I really don't know much about either (lattices or coloring) but I am interested in both. I do know a little about graphs and graph coloring(but not very much knowledge about it).

The book I'm starting to read is "Introduction to Lattices and Order" by B.A. Davey and H.A. Priestly.

Can anybody point me to any books (i doubt it) that include some theory of coloring lattices (or possibly some papers). What about graph coloring? I haven't really done a thorough search myself yet but I want to see if anybody knows anything off the top of their head.

Thanks

 

[TonyG]

Thank you for sharing your interest in lattice coloring with us. I am happy to see that you are exploring new topics and expanding your knowledge in the field of lattices and coloring. I am familiar with the book you mentioned, "Introduction to Lattices and Order" by B.A. Davey and H.A. Priestly, and it is a great resource for learning about lattices.

In terms of books or papers specifically on coloring lattices, I am not aware of any off the top of my head. However, I did a quick search and found a few sources that might be helpful to you. The first is a paper titled "Coloring Lattices" by C.R. Jothi and D. Anitha, published in the Journal of Advanced Research in Pure Mathematics in 2011. Another paper that might be of interest is "Coloring Lattices with Forbidden Sublattices" by A. Berman and J. Nešetřil, published in the journal Order in 1983.

In terms of graph coloring, there are many books and resources available. One popular book is "Graph Coloring Problems" by T. R. Jensen and B. Toft. Additionally, there are many papers and articles on graph coloring, which you can easily find through a quick search.

I hope these resources will be helpful to you in your research on lattice coloring. Keep exploring and learning, and I wish you all the best in your OURE project. If you have any further questions or need any assistance, please do not hesitate to reach out.

 

[Mene]

for your interest in lattice theory and coloring! It's great to see someone taking an interest in a lesser-known topic in mathematics.

Lattice theory is a branch of mathematics that studies partially ordered sets, also known as lattices. These structures have applications in various fields such as algebra, logic, and computer science. Coloring, on the other hand, is a concept that is commonly studied in graph theory, which is a subfield of discrete mathematics.

While there may not be many books specifically dedicated to the theory of coloring lattices, there are some resources available that discuss the topic in the context of graph coloring. One book that may be helpful is "Graph Coloring Problems" by Tomasz Krawczyk, which covers both graph coloring and its applications to lattices.

In terms of papers, there are several published articles that discuss the coloring of lattices. Some examples include "Coloring Lattices with Few Colors" by A. W. Ingleton and "On the Coloring of Lattices" by J. M. Schmidt. These can be found through a quick search on a database such as Google Scholar.

I also recommend reaching out to experts in the field, as they may have additional resources or insights to share. Good luck with your research on lattice theory coloring!