Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps

@article{Bna1997ExactEO,
  title={Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps},
  author={Mikl{\'o}s B{\'o}na},
  journal={J. Comb. Theory, Ser. A},
  year={1997},
  volume={80},
  pages={257-272}
}
Solving the first nonmonotonic, longer-than-three instance of a classic enumeration problem, we obtain the generating function H(x) of all 1342-avoiding permutations of length n as well as an exact formula for their number Sn(1342). While achieving this, we bijectively prove that the number of indecomposable 1342avoiding permutations of length n equals that of labeled plane trees of a certain type on n vertices recently enumerated by Cori, Jacquard and Schaeffer, which is in turn known to be… CONTINUE READING
Highly Influential
This paper has highly influenced 19 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 13 references

The enumeration of permutations with a prescribed number of “forbidden” subsequences

D. Zeilberger, J. Noonan
Advances in Applied Mathematics, 17 • 1996
View 5 Excerpts
Highly Influenced

Symmetric functions and P-recursiveness

J. Comb. Theory, Ser. A • 1990
View 7 Excerpts
Highly Influenced

Asymptotic values for degrees associated with strips of Young diagrams

A. Regev
Advances in Mathematics 41 • 1981
View 6 Excerpts
Highly Influenced

A census of planar maps

J. W. Tutte
Canadian Journal of Mathematics 33 • 1963
View 3 Excerpts
Highly Influenced

S

S. Dulucq
Gire, J. West, Permutations with forbidden subsequences and nonseparable planar maps. Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993), Discrete Math, 153 • 1996
View 1 Excerpt

Forbidden subsequences

Discrete Mathematics • 1994
View 1 Excerpt

Holonomic systems for special functions

D. Zeilberger
J. Computational and Applied Mathematics, 32 • 1990
View 2 Excerpts

Similar Papers

Loading similar papers…