Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
419636 | Discrete Applied Mathematics | 2013 | 4 Pages |
Abstract
Let us call a lattice path in Z×ZZ×Z from (0,0)(0,0) to (n,0)(n,0) using U=(1,k)U=(1,k), D=(1,−1)D=(1,−1), and H=(a,0)H=(a,0) steps and never going below the xx-axis, a (k,a)(k,a)-path (of order nn). A super (k,a)(k,a)-path is a (k,a)(k,a)-path which is permitted to go below the xx-axis. We relate the total number of humps in all of the (k,a)(k,a)-paths of order nn to the number of super (k,a)(k,a)-paths, where a hump is defined to be a sequence of steps of the form UHiDUHiD, i≥0i≥0. This generalizes recent results concerning the cases when k=1k=1 and a=1a=1 or a=∞a=∞. A similar relation may be given involving peaks (consecutive steps of the form UDUD).
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Toufik Mansour, Mark Shattuck,