W.Y.C. Chen, N.Y. Li and L.W. Shapiro,
The butterfly decomposition of plane trees,
Discrete Appl. Math. 155(17) (2007) 2187-2201.

Cited by


  1. W.Y.C. Chen, D.Q.J. Dou and T.Y.J. Zhang, A reflection principle for three vicious walkers, arXiv:0808.1435.

  2. W.Y.C. Chen, D.Q.J. Dou and T.Y.J. Zhang, On three and four vicious walkers, J. Statist. Plann. Inference 141 (2011) 94-101.

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

  4. G.-S. Cheon, H. Kim and L.W. Shapiro, Profiles of ordered trees with mutation and associated Riordan matrices, Linear Algebra Appl. 511 (2016) 296-317.

  5. N.M. Dube, Combinatorial properties of lattice paths, Master Thesis, University of the Witwatersrand, 2017.

  6. S.-P. Eu, S. Seo and H. Shin, Enumerations of vertices among all rooted ordered trees with levels and degrees, Discrete Math. 340 (2017) 2123-2129.

  7. Nancy S.S. Gu, H. Prodinger and S. Wagner, Bijections for a class of labeled plane trees, European J. Combin. 31 (2010) 720-732.

  8. S.H. Li, J. Ma and Y.-N. Yeh, Uniform partition extensions, a generating functions perspective, Sci. China Math. 58 (2015) 2655-2670.

  9. J. Ma, H. Shen and Y.-N. Yeh, Rooted cyclic permutations of lattice paths and uniform partitions, Discrete Math. 338 (2015) 1111-1125.

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

  11. Y. Park and S. Kim, Chung-Feller property of schröder objects, Electron. J. Combin. 23 (2016) Paper 2.34, 14 pp.

  12. L. Salaam, Combinatorial statistics on phylogenetic trees, Ph.D. Thesis, Howard University, 2008.

  13. 马俊, 叶永南, 雷洪川, 均匀划分, 中国科学: 数学 45 (2015) 1389-1402.