Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE ENUMERATION OF DOUBLY ALTERNATING BAXTER PERMUTATIONS

  • Min, Sook (Department of Mathematics College of Liberal Arts and Science Yonsei University) ;
  • Park, Seung-Kyung (Department of Mathematics College of Science Yonsei University)
  • Published : 2006.05.01
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Abstract

In this paper, we give an alternative proof that the number of doubly alternating Baxter permutations is Catalan.

Keywords

References

  1. G. Baxter, On fixed points of the composite of commuting functions, Proc. Amer. Math. Soc. 15 (1964), 851-855
  2. F. R. K. Chung, R. L. Graham, V. E. Hoggatt, Jr., and M. Kleiman, The number of Baxter permutations, J. Combin. Theory Ser. A 24 (1978), no. 3, 382-394 https://doi.org/10.1016/0097-3165(78)90068-7
  3. B. R. Cori, S. Dulucq, and G. Viennot, Shuffle of parenthesis systems and Baxter permutations, J. Combin. Theory Ser. A 43 (1986), no. 1, 1-22 https://doi.org/10.1016/0097-3165(86)90018-X
  4. M. Delest and X. Viennot, Algebraic languages and polyominoes enumeration, Theoret. Comput. Sci. 34 (1984), no. 1-2, 169-206 https://doi.org/10.1016/0304-3975(84)90116-6
  5. S. Dulucq and O. Guibert, Stack words, standard tableaux and Baxter permuta- tions, Discrete Math. 157 (1996), no. 1-3, 91-106 https://doi.org/10.1016/S0012-365X(96)83009-3
  6. S. Dulucq and O. Guibert, Baxter Permutations, Proceedings of the 7th Conference on Formal Power Series and Algebraic Combinatorics conference(Noisy-le-Grand, 1995), Discrete Math. 180 (1998), no. 1-3, 143-156 https://doi.org/10.1016/S0012-365X(97)00112-X
  7. K. Eriksson and S. Linusson, The size of Fulton's essential set, Electron. J. Combin. 2, (1995) R6
  8. K. Eriksson and S. Linusson, Combinatorics of Fulton's essential set, Duke Math. J. 85 (1996), no. 1, 61-76 https://doi.org/10.1215/S0012-7094-96-08502-6
  9. W. Fulton, Flags, Schubert polynomials, degeneracy loci, and determinantal for mulas, Duke Math. J. 65 (1992), no. 3, 381-420 https://doi.org/10.1215/S0012-7094-92-06516-1
  10. I. Gessel and G. Viennot, Binomial determinants, paths, and hook length formu- lae, Adv. in Math. 58 (1985), no. 3, 300-321 https://doi.org/10.1016/0001-8708(85)90121-5
  11. S. Gire, Arbres, permutations a motifs exclus et cartes planaires : quelques problµemes algorithmiques et combinatoires, Ph.D thesis, LaBRI, Universite, Bor- deaux 1, 1993
  12. O. Guibert and S. Linusson, Doubly alternating Baxter permutations are catalan, Discrete Math. 217 (2000), no. 1-3, 157-166 https://doi.org/10.1016/S0012-365X(99)00261-7
  13. C. L. Mallows, Baxter permutations rise again, J. Combin. Theory Ser. A 27 (1979), no. 3, 394-396 https://doi.org/10.1016/0097-3165(79)90034-7
  14. S. Min, On the essential sets of the Baxter and pseudoBaxter permutations, Ph.D. Thesis, Yonsei University, 2002
  15. S. Min and S. Park, The maximal-inversion statistic and pattern avoiding permutations, preprint
  16. G. Viennot, A bijective proof for the number of Baxter permutations, Seminaire Lotharingien de Combinatoire, Le Klebach, 1981