W.Y.C. Chen, S.H.F. Yan and L.L.M. Yang,
Identities from weighted Motzkin paths,
Adv. Appl. Math. 41 (2008) 329-334.

Cited by


  1. P. Barry, On integer-sequence-based constructions of generalized Pascal triangles, J. Integer Seq. 9 (2006) Article 06.2.4, 34 pp.

  2. P. Barry and A. Hennessy, A note on Narayana triangles and related polynomials, Riordan arrays, and MIMO capacity calculations, J. Integer Seq. 14(3) (2011) Article 11.3.8, 26 pp.

  3. R. De Castro, A.L. Ramírez and J.L. Ramírez, Applications in enumerative combinatorics of infinite weighted automata and graphs, Scientific annals of computer science 24(1) (2014) 137-171.

  4. W.Y.C. Chen, E. Deutsch and S. Elizalde, Old and young leaves on plane trees, European J. Combin. 27 (2006) 414-427.

  5. W.Y.C. Chen and S.X.M. Pang, On the combinatorics of the Pfaff identity, Discrete Math. 309 (2009) 2190-2196.

  6. W.Y.C. Chen, A.Y.Z. Wang and A.F.Y. Zhao, Identities derived from noncrossing partitions of type B, Electron. J. Combin. 18 (2011) Paper 129, 17 pp.

  7. Z. Chen and H. Pan, Identities involving weighted Catalan, Schröder and Motzkin paths, Adv. in Appl. Math. 86 (2017) 81-98.

  8. S.K. Choi, C. Rim and H. Um, Narayana number, Chebyshev polynomial and Motzkin path on RNA abstract shapes, Preprint.

  9. T. Došlić and D. Veljan, Secondary structures, plane trees and Motzkin numbers, Math. Commun. 12 (2007) 163-169.

  10. D. Féral and S. Péché, The largest eigenvalues of sample covariance matrices for a spiked population: diagonal case, J. Math. Phys. 50 (2009) 073302.

  11. S.-C. Liu, Y. Wang and Y.-N. Yeh, Chung-Feller property in view of generating functions, Electron. J. Combin. 18 (2011) Paper 104, 20 pp.

  12. S.-M. Ma, J. Ma and Y.-N. Yeh, γ-Positivity and partial γ-positivity of descent-type polynomials, J. Combin. Theory Ser. A 167 (2019) 257-293.

  13. T. Mansour and Y.D. Sun, Identities involving Narayana polynomials and Catalan numbers, Discrete Math. 309 (2009) 4079-4088.

  14. E. Marberg, Actions and identities on set partitions, Electron. J. Combin. 19 (2012) Paper 28, 31 pp.

  15. F. Mezzadri and N.J. Simm, Moments of the transmission eigenvalues, proper delay times and random matrix theory II, J. Math. Phys. 53 (2012) 053504, 42 pp.

  16. H. Pan, Touchard type identity for q-Narayana numbers, J. Combin. Theory Ser. A 188 (2022) Paper No. 105595.

  17. Y. Park, S.K. Park, Enumeration of generalized lattice paths by string types, peaks, and ascents, Discrete Math. 339 (2016) 2652-2659.

  18. S. Péché, Universality at the soft edge for some white sample covariance matrices ensembles, arXiv:0705.1701.

  19. S. Péché , Universality results for the largest eigenvalues of some sample covariance matrix ensembles, Probab. Theory Related Fields 143 (2009) 481-516.

  20. 孙毅, 苏贵福,源自赋权 2-Motzkin 路的组合恒等式及其应用, 山东大学学报 47(6) (2012) 90-94.

  21. 孙怡东, 计数组合学中若干问题的研究, 博士学位论文, 大连理工大学, 2006.