Raney paths and a combinatorial relationship between rooted nonseparable planar maps and two-stack-sortable permutations

Journal of Combinatorial Theory. Series A

Volumn 75, Issue 2, 1996, Pages 220-242

  Goulden, I P ^a   West, J ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030209755     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.1996.0074     Document Type: Article

References (12)

1. 1. W. G. BROWN, Enumeration of non-separable planar maps, Canad. J. Math. 15 (1963), 526-545.
2. 2. W. G. BROWN AND W. T. TUTTE, On the enumeration of rooted non-separable planar maps, Canad. J. Math. 16 (1964), 572-577.
3. 3. S. DULUCQ, S. GIRE, AND O. GUIBERT, A combinatorial proof of J. West's conjecture, preprint.
4. 4. S. DULUCQ, S. GIRE, AND J. WEST, Permutations with forbidden subsequences and rooted nonseparable planar maps, in "Proceedings, Formal Power Series and Algebraic Combinatorics, Florence, 1993;" Discrete Math., to appear.
5. 5. I. M. GESSEL, A noncommutative generalization and q-analog of the Lagrange inversion formula, Trans. Amer. Math. Soc. 257 (1980), 455-481.
6. 6. I. M. GESSEL, Enumerating two-stack-sortable multipermutations, Abstracts Amer. Math. Soc. 15 (1994), 535.
7. 7. I. P. GOULDEN AND D. M. JACKSON, "Combinatorial Enumeration," Wiley, New York, 1983.
8. 8. D. KNUTH, "The Art of Computer Programming, Vol. 1, 2 ed.," Addison-Wesley, Reading, MA, 1973.
9. 9. G. N. RANEY, Functional composition patterns and power series reversion, Trans. Amer. Math. Soc. 94 (1960), 441-451.
10. 10. W. T. TUTTE, A census of planar maps, Canad. J. Math. 15 (1963), 249-271.
11. 11. J. WEST, Permutations with restricted subsequences and stack-sortable permutations, Ph.D. thesis, MIT, 1990.
12. 12. D. ZEILBERGER, A proof of Julian West's conjecture that the number of two-stack-sortable permutations of length n is 2(3n)!/((n + 1)!(2n + 1)!), Discrete Math. 102 (1992), 85-93.