An Introduction to Symmetric Functions and Their Combinatoric... - 9781470448998

An Introduction to Symmetric Functions and Their CombinatoricsAuthor(s): Eric S. Egge\nFormat: Paperback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470448998, 978-1470448998\nSynopsis\nThis book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi-Trudi identities; the involution $omega$; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan-Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood-Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree co.