Two-boundary lattice paths and parking functions Academic Article uri icon

abstract

  • We describe an involution on a set of sequences associated with lattice paths with north or east steps constrained to lie between two arbitrary boundaries. This involution yields recursions (from which determinantal formulas can be derived) for the number and area enumerator of such paths. An analogous involution can be defined for parking functions with arbitrary lower and upper bounds. From this involution, we obtained determinantal formulas for the number and sum enumerator of such parking functions. For parking functions, there is an alternate combinatorial inclusion-exclusion approach. The recursions also yield Appell relations. In certain special cases, these Appell relations can be converted into rational or algebraic generating functions. 2006 Elsevier Inc. All rights reserved.

published proceedings

  • Advances in Applied Mathematics

author list (cited authors)

  • Kung, J., Sun, X., & Yan, C.

citation count

  • 2

complete list of authors

  • Kung, Joseph PS||Sun, Xinyu||Yan, Catherine

publication date

  • January 2007