By Jeffrey Remmel,Anthony Mendes
This monograph presents a self-contained creation to symmetric features and their use in enumerative combinatorics. it's the first e-book to discover the various tools and effects that the authors current. quite a few workouts are incorporated all through, in addition to complete strategies, to demonstrate strategies and in addition spotlight many attention-grabbing mathematical ideas.
The textual content starts through introducing primary combinatorial items akin 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 suggestions are prolonged to discover producing capabilities for quite a few items 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, protecting consecutive development suits in variations, phrases, cycles, and alternating variations and introducing the reciprocity strategy with a view to outline ring homomorphisms with fascinating properties.
Counting with Symmetric Functions will attract graduate scholars and researchers in arithmetic or similar topics who're drawn to counting equipment, producing features, or symmetric functions. the original strategy taken and effects and workouts explored by way of the authors make it a tremendous contribution to the mathematical literature.
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Additional info for Counting with Symmetric Functions (Developments in Mathematics)
Counting with Symmetric Functions (Developments in Mathematics) by Jeffrey Remmel,Anthony Mendes