W.Y.C. Chen,
Context-free grammars, differential operator and formal power series,
Theoret. Comput. Sci. 117 (1993) 113-129.

Cited by

  1. J.F. Barbero G., J. Salas and E.J.S. Villaseñor, Generalized Stirling permutations and forests: Higher-order Eulerian and Ward numbers, Electron. J. Combin. 22 (2015) Paper 3.37, 20 pp.

  2. Y. Cai, New perspectives of quantum analogues, Ph.D. Thesis, University of Kentucky, 2016.

  3. Y. Cai, R. Ehrenborg and M. Readdy, q-Stirling identities revisited, Electron. J. Combin. 25 (2018) Paper 1.37, 18 pp.

  4. D. Callan, S.-M. Ma and T. Mansour, Some combinatorial arrays related to the Lotka-Volterra system, Electron. J. Combin. 22 (2015) Paper 2.22, 12 pp.

  5. X. Chen and A.D. Sokal, Total positivity of some polynomial matrices that enumerate labeled trees and forests, arXiv:2302.03999v1.

  6. W.Y.C. Chen and A.M. Fu, Context-free grammars for permutations and increasing trees, Adv. in Appl. Math. 82 (2017) 58-82.

  7. W.Y.C. Chen and V.J.W. Guo, Bijections behind the Ramanujan polynomials, Adv. in Appl. Math. 27 (2001) 336-356.

  8. W.Y.C. Chen, R.X.J. Hao and H.R.L.Yang, Context-free grammars and multivariate stable polynomials over Stirling permutations, In: V. Pillwein and C. Schneider (eds.), Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, pp. 109-135, Springer, 2021.

  9. W.Y.C. Chen, K.-W. Lih and Y.-N. Yeh, Cyclic tableaux and symmetric functions, Stud. Appl. Math. 94 (1995) 327-339.

  10. W.Y.C. Chen and J.D. Louck, The combinatorial power of the companion matrix, Linear Algebra Appl. 232 (1996) 261-278.

  11. W.Y.C. Chen and H.R.L. Yang, A context-free grammar for the Ramanujan-Shor polynomials, Adv. in Appl. Math., 126 (2021) 101908.

  12. R. De Castro, A. Ramírez and J.L. Ramírez, Applications in enumerative combinatorics of infinite weighted automata and graphs, Sci. Ann. Comput. Sci. 24 (2014) 137-171.

  13. A. De Médicis and P.Leroux, Generalized Stirling numbers, convolution formulae and p, q-analogues, Can. J. Math. 47 (1995) 474-499.

  14. A. Di Bucchianico and D. Loeb, A selected survey of umbral calculus, Electron. J. Combin. 2 (2000) Dynamic Survey 3, 34 pp.

  15. D. Dumont and A. Ramamonjisoa, Grammaire de Ramanujan et arbres de Cayley, Electron. J. Combin. 3 (1996) Research Paper 17, 18 pp.

  16. R. Ehrenborg, On apolarity and generic canonical forms, J. Algebra 213 (1999) 167-194.

  17. R. Ehrenborg, Generating functions for the cd-indices of simplices and cubes, Enumer. Comb. Appl. 4(3) (2024) Article #S2R17.

  18. D. Foata, Dominique Dumont (1947-2016), Sém. Lothar. Combin. 76 ([2016-2017]) Art. B76z, 6 pp.

  19. A.M. Fu, A context-free grammar for peaks and double descents of permutations, Adv. in Appl. Math. 100 (2018) 179-196.

  20. A.M. Fu and F.Z.K. Li, Joint distributions of permutation statistics and the parabolic cylinder functions, European J. Combin., 85 (2020) 103060.

  21. V.J.W. Guo, A bijective proof of the Shor recurrence, European J. Combin. 70 (2018) 92-98.

  22. G.-N. Han and S.-M. Ma, Derivatives, Eulerian polynomials and the g-indexes of Young tableaux, arXiv:2006.14064.

  23. R.X.J. Hao, L.X.W. Wang and H.R.L. Yang, Context-free grammars for triangular arrays, Acta Math. Sin. ( Engl. Ser. ) 31 (2015) 445-455.

  24. C. Hespel, Iterated derivatives of the output of a nonlinear dynamic system and Faà di Bruno formula, Math. Comput. Simulation 42 (1996) 641-657.

  25. L.C. Hsu and P.J.S. Shiue, Cycle indicators and special functions, Ann. Comb. 5 (2001) 179-196.

  26. W.P. Johnson, Some applications of the q-exponential formula, Discrete Math. 157 (1996) 207-225.

  27. W.P. Johnson, The curious history of Faà di Bruno's formula, Amer. Math. Monthly 109 (2002) 217-234.

  28. Zhicong Lin and Jun Ma, A symmetry on weakly increasing trees and multiset Schett polynomials, arXiv:2104.10539v1.

  29. Zhicong Lin, Jun Ma and Philip B. Zhang, Statistics on multipermutations and partial $\gamma$-positivity, J. Combin. Theory Ser. A, 183 (2021), 105488.

  30. S.-M. Ma, Enumeration of permutations by number of alternating runs, Discrete Math. 313 (2013) 1816-1822.

  31. S.-M. Ma, On γ-vectors and the derivatives of the tangent and sectant functions, Bull. Aust. Math. Soc. 90 (2014) 177-185.

  32. S.-M. Ma, Some combinatorial sequences associated with context-free grammars, arXiv:1208.3104.

  33. S.-M. Ma, Some combinatorial arrays generated by context-free grammars, European J. Combin. 34 (2013) 1081-1091.

  34. Shi-Mei Ma, Qi Fang, Toufik Mansour and Yeong-Nan Yeh, Alternating Eulerian polynomials and left peak polynomials, Discrete Math. 345(3) (2022) Paper No. 112714.

  35. S.-M. Ma, J. Ma, Jean Yeh and Y.-N. Yeh, The e-positivity of multivariate k-order Eulerian polynomials, arXiv:2106.16189v1.

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

  37. S.-M. Ma, J. Ma and Y.-N. Yeh, On certain combinatorial expansions of descent polynomials and the change of grammars, arXiv:1802.02861.

  38. S.-M. Ma, J. Ma and Y.-N. Yeh, On certain combinatorial expansions of the Legendre-Stirling numbers, arXiv:1805.10998.

  39. S.-M. Ma, J. Ma and Y.-N. Yeh, The ascent-plateau statistics on Stirling permutations, arXiv:1801.08056.

  40. S.-M. Ma, J. Ma, Y.-N. Yeh and B.-X. Zhu, Context-free grammars for several polynomials associated with Eulerian polynomials, Electron. J. Combin. 25 (2018) Paper 1.31, 17 pp.

  41. S.-M. Ma, T. Mansour and M. Schork, Normal ordering problem and the extensions of the Stirling grammar, Russ. J. Math. Phys. 21 (2014) 242-255.

  42. S.-M. Ma, T. Mansour and D.G.L. Wang, Combinatorics of Dumont differential system on the Jacobi elliptic functions, arXiv:1403.0233.

  43. S.-M. Ma, H. Qi, J. Yeh and Y.-N. Yeh, Stirling permutation codes, J. Combin. Theory Ser. A 199 (2023) Paper No. 105777.

  44. S.-M. Ma, H. Qi, J. Yeh and Y.-N. Yeh, On the joint distributions of succession and Eulerian statistics, arXiv:2401.01760.

  45. S.-M. Ma and H.-N. Wang, Enumeration of a dual set of Stirling permutations by their alternating runs, Bull. Aust. Math. Soc. 94 (2016) 177-186.

  46. S.-M. Ma and Y.-N. Yeh, Eulerian polynomials, Stirling permutations of the second kind and perfect matchings, Electron. J. Combin. 24 (2017) Paper 4.27, 18 pp.

  47. R.S. Maier, Triangular recurrences,generalized Eulerian numbers, and related number triangles. arXiv:2207.10224v1.

  48. T. Mansour and M. Schork, Commutation Relations, Normal Ordering, and Stirling Numbers, CRC Press, 2016.

  49. M.A. Méndez, Combinatorial differential operators in: Faà di Bruno formula, enumeration of ballot paths, enriched rooted trees and increasing rooted trees, arXiv:1610.03602.

  50. N.E. Oussous, Contribution à l'identification de modèles par l'algèbre non commutative, Habilitation Thesis, Universite des Sciences et Technologies de Lille, 2001.

  51. J.L. Ramírez, M.A. Méndez, A new approach to the r-Whitney numbers by using combinatorial differential calculus, arXiv:1702.06519.

  52. B. Randrianirina, Espèces mixtes et systèmes d'équations différentielles, Annales des sciences mathématiques du Québec. Université du Québec à Montréal, Département de mathématiques et informatique, 24 (2000) 179-211.

  53. T.J. Robinson, Formal calculus, umbral calculus, and basic axiomatics of vertex algebras, Ph.D. Thesis, The State University of New Jersey, 2009.

  54. T.J. Robinson, Formal calculus and umbral calculus, Electron. J. Combin. 17 (2010) Research Paper 95, 31 pp.

  55. J.L. Schofield, Representation of special polynomials by the cycle indicator, Master Thesis, University of Nevada, 2002.

  56. A. Sokal, Positivity problems at the boundary between combinatorics and analysis, EPSRC-funded research project, 2016-2021.

  57. A. Sokal, Total positivity of some polynomial matrices that enumerate labeled trees and forests, arXiv:2105.05583v1, 2021.

  58. J. Triana and R. De Castro, Binomial coefficients and multifactorial numbers through generative grammars, arXiv:1808.06313.

  59. B.-X. Zhu, Y.-N. Yeh and Q. Lu, Context-free grammars, generating functions and combinatorial arrays, European J. Combin. 78 (2019) 236-255.

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