Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent WorkJoseph P.S. Kung Elsevier, 12 de maig 2014 - 342 pàgines Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardson rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra. |
Altres edicions - Mostra-ho tot
Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology ... Joseph P. S. Kung Visualització de fragments - 1982 |
Frases i termes més freqüents
antichains basis Baxter operators Baxter sequence bitableau Capelli operator cell characteristic-free coefficient column Combinatorial Theory commutative ring complexe consider construction coordinate ring corollary corresponding decreasing subsequences defined denote deux Doubilet element entries example Ferrers diagram foncteurs fundamental theorem given GL(m GL(n grassmannienne Hence hook lengths ideal induction inner products insertion invariant theory isomorphe k-family k-increasing Lemma LEMME letter place algebras lexicographic linear combination linear independence Math Mathematics matrix monomial morphisme multitableaux notation numbering of F obtained paper partially ordered set permutation Pfaffians plane partitions polynomial Proposition prove Q-symbol of F(A R-basis representation theory résolution resp result Rota satisfying Schensted Schensted's algorithm Schur functions Section shuffle product skew Specht squares standard bideterminants standard numbering standard tableaux straightening formula subset suite spectrale Suppose symétriques symmetric group tableau tableaux of shape Theorem 3.1 variables variété de Schubert vector Young diagrams Young tableaux zero