By Jeffrey Remmel,Anthony Mendes
This monograph offers a self-contained advent to symmetric capabilities and their use in enumerative combinatorics. it's the first ebook to discover a number of the equipment and effects that the authors current. a number of workouts are incorporated all through, in addition to complete options, to demonstrate options and likewise spotlight many fascinating mathematical ideas.
The textual content starts off by means of introducing primary combinatorial gadgets reminiscent of variations and integer walls, in addition to producing functions. Symmetric features 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 capabilities for permutation records, after which those recommendations are prolonged to discover producing features for a number of 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 expert than the previous ones, masking consecutive trend fits in variations, phrases, cycles, and alternating diversifications and introducing the reciprocity strategy with a view to outline ring homomorphisms with fascinating properties.
Counting with Symmetric Functions will entice graduate scholars and researchers in arithmetic or comparable matters who're drawn to counting equipment, producing services, or symmetric functions. the original technique taken and effects and workouts explored via the authors make it a major contribution to the mathematical literature.
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Extra resources for Counting with Symmetric Functions (Developments in Mathematics)
Counting with Symmetric Functions (Developments in Mathematics) by Jeffrey Remmel,Anthony Mendes