Items related to Algebraic Combinatorics: Walks, Trees, Tableaux, and...
Synopsis
Preface.- Notation.- 1. Walks in graphs.- 2. Cubes and the Radon transform.- 3. Random walks.- 4. The Sperner property.- 5. Group actions on boolean algebras.- 6. Young diagrams and q-binomial coefficients.- 7. Enumeration under group action.- 8. A glimpse of Young tableaux.- Appendix. The RSK algorithm.- Appendix. Plane partitions.- 9. The Matrix-Tree Theorem.- Appendix. Three elegant combinatorial proofs.- 10. Eulerian diagraphs and oriented trees.- 11. Cycles, bonds, and electrical networks.- 12. Miscellaneous gems of algebraic combinatorics.- Hints.- References.
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About the Author
Professor Richard Stanley is one of the most well-known algebraic combinatorists in the world. He is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Amongst his several visiting professorships, Stanley has received numerous awards including the George Polya Prize in Applied Combinatorics, Guggenheim Fellowship, admission to both the American Academy and National Academies of Sciences, Leroy P. Steele Prize for Mathematical Exposition, Rolf Schock Prize in Mathematics, Senior Scholar at Clay Mathematics Institute, Aisenstadt Chair, Honorary Doctor of Mathematics from the University of Waterloo, and an honorary professorship at the Nankai University. Professor Stanley has had over 50 doctoral students and is well known for his excellent teaching skills. Stanley’s list of publications amount to over 155.
Review
“The chosen topics represent a sample of enumerative combinatorics suitable for the elementary algebra available to an undergraduate student. ... This is a book that can be used to teach a topics course for senior undergraduates. It will help them to solidify their just-acquired abstract algebra and at the same it will introduce them to some beautiful topics in pure or applied combinatorics.” (Felipe Zaldivar, MAA Reviews, maa.org, December, 2015)
“This gentle book provides the perfect stepping-stone up. The various chapters treat diverse topics ... . Stanley’s emphasis on ‘gems’ unites all this--he chooses his material to excite students and draw them into further study. ... Summing Up: Highly recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 51 (8), April, 2014)"About this title" may belong to another edition of this title.
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