충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제35권4호
  • /
  • Pages.335-343
  • /
  • 2022
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

FUSS-NARAYANA STATISTICS

  • Kim, Sangwook (Department of Mathematics Chonnam National University)
  • 투고 : 2022.10.11
  • 심사 : 2022.11.08
  • 발행 : 2022.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We show that valleys, high peaks, and modular ascents are statistics of Fuss-Catalan paths having a distribution given by the Fuss-Narayana number. We prove the results using the Cycle Lemma and provide bijections among them. We also show that relative peaks are independent of the base path. In particular, valleys and high peaks can be obtained from relative peaks by fixing the base path in certain ways.

키워드

과제정보

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1F1A1062356).

참고문헌

  1. P. Branden, q-Narayana numbers and the flag h-vector of J(2×n), Discrete Math., 281 (2004), 67-81. https://doi.org/10.1016/j.disc.2003.07.006
  2. J. Cigler, Some remarks on Catalan families, European J. Combin., 8 (1987), 261-267. https://doi.org/10.1016/s0195-6698(87)80030-6
  3. A. Dvoretzky and T. Motzkin, A problem of arrangements, Duke Math. J., 14 (1947), 305-313. https://doi.org/10.1215/S0012-7094-47-01423-3
  4. A. Huq, Generalized Chung-Feller theorems for lattice paths, PhD thesis, 2009. Thesis (Ph.D.)-Brandeis University.
  5. R. A. Sulanke, Constraint-sensitive Catalan path statistics having the Narayana distribution, Discrete Math., 204 (1999), 397-414. https://doi.org/10.1016/S0012-365X(98)00382-3
  6. R. A. Sulanke, The Narayana distribution. Special issue on lattice path combinatorics and applications (Vienna, 1998), J. Statist. Plann. Inference, 101 (2002), 311-326. https://doi.org/10.1016/S0378-3758(01)00192-6