논문KCI 등재
Avoiding permutations and the Narayana numbers
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We study 132 avoiding permutations that also avoid (2r +1)(2r+2) · · · 12 but contain (2r−1)(2r) · · · 12 pattern. We find an identitybetween the number of these permutations and the Narayana number. Wealso present relations between 132 avoiding permutations and polygondissections. Finally, a generalization of these permutations is obtained.
Abstract
We study 132 avoiding permutations that also avoid (2r +1)(2r+2) · · · 12 but contain (2r−1)(2r) · · · 12 pattern. We find an identitybetween the number of these permutations and the Narayana number. Wealso present relations between 132 avoiding permutations and polygondissections. Finally, a generalization of these permutations is obtained.
참고문헌 (6)
- D. Callan, "Kreweras’ Narayana Number Identity Has a Simple Dyck Path Interpretation", ~ (2005)
- D. Callan, "Polygon Dissections and marked Dyck Paths", ~ (2005)
- C. Krattenthaler, "Permutations with restricted patterns and Dyck paths", Adv. in Appl. Math, 27(2-3), pp.510~530 (2001)
- "On-line Encyclopedia of Integer Sequences"[URL]
- R. A. Sulanke, "Generalizing Narayana and Schr¨oder Numbers to Higher Dimensions", The Electronic Journal of Combinatorics, 11 (2004)
- J. West, "Generating trees and forbidden subsequences", Discrete Math, 157(1-3), pp.363~374 (1996)
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