Stanley R.P. Algebraic Combinatorics. Walks, Trees, Tableaux and more

2nd edition. — New York: Springer, 2018. — 263 p.The primary change from the first edition is the addition of a chapter entitled “A Glimpse of Combinatorial Commutative Algebra” (Chapter 12). Writing this chapter was an interesting challenge. The “standard” applications of commutative algebra to combinatorics require a background in algebraic topology and homological algebra. I wanted to give a substantial application without using these two subjects and without developing a lot of commutative algebra. It was still necessary to present quite a bit of material on simplicial complexes so that the main result (Theorem 12.25) can be adequately appreciated. The result has been that Chapter 12 is the longest chapter in the book. I hope that I have succeeded in giving some of the flavor of the remarkable connections between commutative algebra and the combinatorics of simplicial complexes.
I have also added a section to Chapter 13 (Section 13.8) involving commutative algebra, but at a much simpler level than Chapter 12. A few new exercises have been added throughout the book, and numerous typos and minor inaccuracies have been corrected. There is now too much material for a one-semester course. The instructor therefore has the pleasure of choosing among diverse treasures, while the student has something to look forward to when the course has ended