Counting with Symmetric Functions (Developments in by Jeffrey Remmel,Anthony Mendes PDF

By Jeffrey Remmel,Anthony Mendes

This monograph offers a self-contained advent to symmetric features and their use in enumerative combinatorics.  it's the first ebook to discover the various equipment and effects that the authors current. a number of routines are integrated all through, in addition to complete recommendations, to demonstrate recommendations and likewise spotlight many fascinating mathematical ideas.

The textual content starts off by way of introducing basic combinatorial gadgets comparable to diversifications and integer walls, in addition to producing functions.  Symmetric services are thought of within the subsequent bankruptcy, with a special emphasis at the combinatorics of the transition matrices among bases of symmetric functions.  bankruptcy three makes use of this introductory fabric to explain how to define an collection of producing features for permutation statistics, after which those concepts are prolonged to discover producing services for numerous gadgets in bankruptcy 4.  the following chapters current the Robinson-Schensted-Knuth set of rules and a mode for proving Pólya’s enumeration theorem utilizing symmetric functions.  Chapters 7 and eight are extra really good than the previous ones, protecting consecutive development suits in diversifications, phrases, cycles, and alternating diversifications and introducing the reciprocity approach to be able to outline ring homomorphisms with fascinating properties.

Counting with Symmetric Functions will entice graduate scholars and researchers in arithmetic or similar matters who're drawn to counting equipment, producing features, or symmetric functions.  the original strategy taken and effects and workouts explored by means of the authors make it a massive contribution to the mathematical literature.

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