This work consists of two independent parts. The first part deals with deformations of the usual basis of symmetric functions using techniques of umbral calculus. As main result the author obtains a characterization of all possible bases for the ring of symmetric functions for which the Littlewood--Richardson coefficients arise as structure coefficients. The second part solves a ten years old conjecture concerning Macdonald polynomials: the Kawanaka Macdonald polynomial conjecture.
This work consists of two independent parts. The first part deals with deformations of the usual basis of symmetric functions using techniques of umbral calculus. As main result the author obtains a characterization of all possible bases for the ring of symmetric functions for which the Littlewood--Richardson coefficients arise as structure coefficients. The second part solves a ten years old conjecture concerning Macdonald polynomials: the Kawanaka Macdonald polynomial conjecture.
This is a paperback version of the second, much expanded, edition of Professor Macdonald's acclaimed monograph on symmetric functions and Hall polynomials. Almost every chapter has new sections and...
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the...
This volume contains the proceedings of the NATO Advanced Study Institute "Symmetric Functions 2001: Surveys of Developments and Per spectives", held at the Isaac Newton Institute for Mathematical...
This work offers detailed coverage of every important aspect of symmetric structures in function of a single real variable, providing a historical perspective, proofs and useful methods for...
This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis...
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