Orientations, Semiorders, Arrangements, and Parking Functions
Copyright policy )Orientations, Semiorders, Arrangements, and Parking Functions
It is known that the Pak-Stanley labeling of the Shi hyperplane arrangement provides a bijection between the regions of the arrangement and parking functions. For any graph $G$, we define the $G$-semiorder arrangement and show that the Pak-Stanley labeling of its regions produces all $G$-parking functions.
- Reed College United States
hyperplane arrangements, 52C35, 05C25, FOS: Mathematics, Mathematics - Combinatorics, semiorders, abelian sandpile model, Combinatorics (math.CO), parking functions, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Graphs and abstract algebra (groups, rings, fields, etc.)
hyperplane arrangements, 52C35, 05C25, FOS: Mathematics, Mathematics - Combinatorics, semiorders, abelian sandpile model, Combinatorics (math.CO), parking functions, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Graphs and abstract algebra (groups, rings, fields, etc.)
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