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Set maps, umbral calculus, and the chromatic polynomial
Algebra & Discrete Mathematics| Speaker: | Gus Wiseman, UC Davis |
| Location: | 693 Kerr |
| Start time: | Mon, Apr 25 2005, 3:10PM |
Description
Some important properties of the chromatic polynomial also hold for any
polynomial set map satisfying a certain binomial type identity. Using
elementary umbral calculus, we give a formula for the expansion of such a
set map in terms of any associated sequence (or Sheffer sequence).
Applications to graph coloring are numerous, including several new
expansions of the chromatic polynomial. By extending associated sequences to
symmetric function bases, we also obtain corresponding expansions of the
chromatic symmetric function.