W.Y.C. Chen, L.W. Shapiro and L.L.M. Yang,
Parity reversing involutions on plane trees and 2-Motzkin paths,
European J. Combin. 27(2) (2006) 283-289.

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  1. 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.

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  3. S.-P. Eu, T.-S. Fu, Y.-J. Pan and C.-T. Ting, Sign-balance identities of Adin-Roichman type on 321-avoiding alternating permutations, Discrete Math. 312 (2012) 2228-2237.

  4. N.S.S. Gu, A parity reversing involution on plane trees, 中国科技论文在线.

  5. L. Guo, Operated semigroups, Motzkin paths and rooted trees, J. Algebraic Comb. 29 (2009) 35-62.

  6. N.Y. Li and T. Mansour, An identity involving Narayana numbers, European J. Combin. 29 (2008) 672-675.

  7. S.X.M. Pang and L. Lv, A combinatorial proof for identities on an odd number and an even number of right leaves in p-ary trees, Information Technology Journal 13 (2014) 1459-1462.

  8. S.G. Wagner, Almost all trees have an even number of independent sets, Electron. J. Combin. 16 (2009) Research Paper 93, 10 pp.

  9. S.G. Wagner and H. Wang, On the parity of the Wiener index, European J. Combin. 30 (2009) 996-1004.