Combinatorial Statistics on Alternating Permutations

1. G. Andrews, “A theorem on reciprocal polynomials with applications to permutations and compositions,” Amer. Math. Monthly 82 (1975), 830-833.

   Google Scholar 

2. G. Baxter, “On fixed points of the composite of commuting functions,” Proc. Amer. Math. Soc. 15 (1967), 851-855.

   Google Scholar 

3. A. Björner, “Shellable and Cohen-Macaulay partially ordered sets,” Trans. Amer. Math. Soc. 260 (1980), 159-183.

   Google Scholar 

4. A. Björner, A. Garsia, and R. Stanley, “An introduction to Cohen-Macaulay partially ordered sets,” in Ordered Sets (NATO Adv. Study Inst. Ser. C: Math. Phys. Sci.), Ivan Rival (Ed.), Reidel, Dordrecht/Boston, 1982.

   Google Scholar 

5. J. Bonin, L. Shapiro, and R. Simion, “Some q-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths,” J. Stat. Planning and Inference 34(1993), 35-55.

   Google Scholar 

6. F. Chung, R. Graham, V. Hoggatt, and M. Kleiman, “The number of Baxter permutations,” J. Combin. Theory Series A 24 (1978), 382-394.

   Google Scholar 

7. L. Comtet, Advanced Combinatorics, Reidel, Dordrecht, 1974.

   Google Scholar 

8. R. Cori, “Un code pour les graphes planaires et ses applications,” Asterisque 27, Société Mathématique de France, 1975.

9. R. Cori, S. Dulucq, and X. Viennot, “Shuffle of parenthesis systems and Baxter permutations,” J. Combin. Theory Series A 43 (1986), 1-22.

   Google Scholar 

10. R. Cori and A. Machi, “Maps, hypermaps and their automorphisms: A survey, I, II, III,” Exposition. Math. 10 (1992), 403-427, 429-447, 449-467.

    Google Scholar 

11. M. Delest, “Algebraic languages: A bridge between combinatorics and computer science,” in Algebraic Combinatorics-Formal Power Series and Algebraic Combinatorics/Séries Formelles et Combinatoire Algébrique 1994, L. Billera, C. Greene, R. Simion, and R. Stanley (Eds.), AMS/DIMACS, 24 (1996), 71-87.

12. P. Edelman, “Multichains, noncrossing partitions and trees,” Discr. Math. 40 (1982), 171-179.

    Google Scholar 

13. P. Edelman and R. Simion, “Chains in the lattice of non-crossing partitions,” Discrete Math. 126 (1994), 107-119.

    Google Scholar 

14. D. Jackson, “The lattice of noncrossing partitions and the Birkhoff-Lewis equations,” Waterloo Research Report #89-34, 1989, and European J. Combin. 15 (1994), 245-250.

    Google Scholar 

15. G. Kreweras, “Sur les partitions noncroisées d'un cycle,” Discrete Math. 1 (1972), 333-350.

    Google Scholar 

16. C. Lee, “The associahedron and triangulations of the n-gon,” European J. Combin. 10 (1989), 551-560.

    Google Scholar 

17. C.L. Mallows, “Baxter permutations rise again,” J. Combin. Theory Series A 27 (1979), 394-396.

    Google Scholar 

18. R. Mullin, “The enumeration of Hamiltonian polygons,” Pacific J. Math. 16 (1966), 139-145.

    Google Scholar 

19. I. Niven, “A combinatorial problem of finite sequences,” Nieuw Arch. Wisk. 16 (1968), 116-123.

    Google Scholar 

20. D.G. Rogers and L. Shapiro, “Dequeues, trees, and lattice paths,” in Lecture Notes in Mathematics, K.L. McAvaney (Ed.), Vol. 884, pp. 293-303, Springer-Verlag, New York, 1981.

    Google Scholar 

21. R. Simion and D. Ullman, “On the structure of the lattice of noncrossing partitions,” Discrete Math. 98 (1991), 193-206.

    Google Scholar 

22. R. Stanley, Enumerative Combinatorics, Vol. 1, Wadsworth & Brooks/Cole, Monterey, California, 1986.

    Google Scholar 

23. W.T. Tutte, “A census of Hamiltonian polygons,” Canad. J. Math. 14 (1962), 402-417.

    Google Scholar 

24. T.R.S. Walsh and A.B. Lehman, “Counting rooted maps by genus, I, II, III,” J. Combin. Theory 13 (1972), 122-141, 192-218, and 18(1975), 259.

    Google Scholar 

25. J.W.T. Youngs, “Minimal imbeddings and the genus of a graph,” J. Math. Mech. 12 (1963), 303-315.

    Google Scholar 

26. G. Ziegler, “Lectures on polytopes,” Graduate Texts in Mathematics # 152, Springer-Verlag, New York, 1995.

    Google Scholar 

Download references