scholarly journals Root polytopes, parking functions, and the HOMFLY polynomial

10.4171/qt/89 ◽  
2017 ◽  
Vol 8 (2) ◽  
pp. 205-248 ◽  
Author(s):  
Tamás Kálmán ◽  
Hitoshi Murakami
Keyword(s):  
Parking Functions ◽  
Homfly Polynomial

scholarly journals THE HOMFLY POLYNOMIAL FOR LINKS IN RATIONAL HOMOLOGY 3-SPHERES

Topology ◽  
1999 ◽  
Vol 38 (1) ◽  
pp. 95-115 ◽  
Author(s):  
Efstratia Kalfagianni ◽  
Xiao-Song Lin
Keyword(s):  
Homfly Polynomial ◽  
Rational Homology

scholarly journals Orientations, Semiorders, Arrangements, and Parking Functions

10.37236/2684 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Sam Hopkins ◽  
David Perkinson
Keyword(s):  
Hyperplane Arrangement ◽  
Parking Functions ◽  
Its Regions

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.

scholarly journals A Decomposition of Parking Functions by Undesired Spaces

10.37236/5940 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Melody Bruce ◽  
Michael Dougherty ◽  
Max Hlavacek ◽  
Ryo Kudo ◽  
Ian Nicolas
Keyword(s):  
Parking Functions ◽  
Partition Lattice ◽  
Self Duality ◽  
Noncrossing Partition ◽  
Symmetric Chain Decomposition ◽  
Order Complexes ◽  
Maximal Chains ◽  
Symmetric Chain ◽  
Noncrossing Partition Lattice

There is a well-known bijection between parking functions of a fixed length and maximal chains of the noncrossing partition lattice which we can use to associate to each set of parking functions a poset whose Hasse diagram is the union of the corresponding maximal chains. We introduce a decomposition of parking functions based on the largest number omitted and prove several theorems about the corresponding posets. In particular, they share properties with the noncrossing partition lattice such as local self-duality, a nice characterization of intervals, a readily computable Möbius function, and a symmetric chain decomposition. We also explore connections with order complexes, labeled Dyck paths, and rooted forests.

scholarly journals Hopf algebras and dendriform structures arising from parking functions

2007 ◽  
Vol 193 (3) ◽  
pp. 189-241 ◽  
Author(s):  
Jean-Christophe Novelli ◽  
Jean-Yves Thibon
Keyword(s):  
Hopf Algebras ◽  
Parking Functions

scholarly journals Interval parking functions

2021 ◽  
Vol 123 ◽  
pp. 102129
Author(s):  
Emma Colaric ◽  
Ryan DeMuse ◽  
Jeremy L. Martin ◽  
Mei Yin
Keyword(s):  
Parking Functions
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