Enumeration of S-Motzkin paths from left to right and from right to left: a kernel method approach

[1] C. Banderier and B. Gittenberger, Analytic combinatorics of lattice paths: enumeration and asymptotics for the area, Discrete Math. Theor. Comput. Sci. Proc., AG (2006) 345–355.Search in Google Scholar

[2] P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 2009.10.1017/CBO9780511801655Search in Google Scholar

[3] I. M. Gessel and G. Xin, The generating function of ternary trees and continued fractions, Electron. J. Combin., 13 (2006) #R53, 48 pp.10.37236/1079Search in Google Scholar

[4] H. Gould, The Girard-Waring power sum formulas for symmetric functions and Fibonacci sequences, Fibonacci Quart., 37 (1999) 135–140.Search in Google Scholar

[5] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1999.Search in Google Scholar

[6] C. Krattenthaler, Lattice path enumeration, in: Handbook of enumerative combinatorics, Discrete Math. Appl. (Boca Raton), pp. 589–678. CRC Press, Boca Raton, FL, 2015.Search in Google Scholar

[7] H. Mularczyk, Lattice paths and pattern-avoiding uniquely sorted permutations, at https://arxiv.org/abs/1908.04025.Search in Google Scholar

[8] E. Pergola, Two bijections for the area of Dyck paths, Discrete Math., 241 (2001) 435–447.Search in Google Scholar

[9] E. Pergola, R. Pinzani, S. Rinaldi and R. A. SulankeA bijective approach to the area of generalized Motzkin paths, Adv. in Appl. Math., 28 (2002) 580–591.Search in Google Scholar

[10] F. Petrov and A. Vershik, International mathematics competition: Day 2 problem 8, at /imc-math.ddns.net/pdf/imc2018-day2-questions.pdf.Search in Google Scholar

[11] H. Prodinger, S. J. Selkirk and S. Wagner, On two subclasses of Motzkin paths and their relation to ternary trees, in: V. Pillwein and C. Schneider (Eds.), Algorithmic Combinatorics – Enumerative Combinatorics, Special Functions and Computer Algebra in honour of Peter Paule on his 60th birthday, Springer, 2020, pp. 297–316.10.1007/978-3-030-44559-1_15Search in Google Scholar

[12] R. Vidunas, A generalization of Clausen’s identity, Ramanujan J., 26 (2011) 133–146.Search in Google Scholar