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Fast recognition of Baxter permutations using syntactical and complete bipartite composite dag's

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Abstract

A correspondence is developed between permutations and two-dimensional digraphs. When the graphs are also required to be completely bipartite composite (CBC), their permutations then correspond to a class called the Baxter permutations. A permutation can be tested for the Baxter condition by a linear time processing of its digraph. This processing involves a pair of traversals of the digraph and is made possible by exploiting a relationship with the syntactical graphs used in language theory.

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References

  1. R. Alter and J. M. Hart, “Enumerating syntactical graphs and lattices of derivations,”Internat. J. Comp. Inform. Sci. 8 (4): 261–277 (1979).

    Google Scholar 

  2. G. Baxter, “On fixed points of the composite of computing functions,”Proc. Amer. Math. Soc. 15:851–855 (1964).

    Google Scholar 

  3. W. M. Boyce, “Generation of a class of permutation associated with commuting functions,”Math. Algorithms 2:19–26 (1967).

    Google Scholar 

  4. W. M. Boyce, “Baxter permutations and functional composition” (submitted for publication).

  5. F. R. K. Chung, R. L. Graham, V. E. Hoggatt and M. Kleiman, “The number of Baxter permutations,”J. Combinatorial Theory (Series A)24:382–394 (1978).

    Google Scholar 

  6. J. M. Hart, “Derivation languages and syntactical categories,”Inform. Control 28:204–220 (1975).

    Google Scholar 

  7. J. M. Hart, “Doubly keyed lists for binary relations,”Proceedings of the CISS, The Johns Hopkins University, Baltimore, Maryland (1979), pp. 257–261.

    Google Scholar 

  8. J. M. Hart and R. Alter, “Counting Baxter Permutations with Doubly Ordered Graphs,” TR #46-78, Department of Computer Science, University of Kentucky, Lexington, Kentucky (1978).

    Google Scholar 

  9. T. Kamimura and G. Slutzki,Parallel and Two-Way Recognizers of Directed Acyclic Graphs, Lecture Notes in Computer Science #74 (Springer-Verlag, Berlin, 1979), pp. 317–325.

    Google Scholar 

  10. E. Horowitz and S. Sahni,Fundamentals of Data Structures (Computer Science Press, Woodland Hills, California, 1976).

    Google Scholar 

  11. J. Valdes, “Parsing Flowcharts and Series-Parallel Graphs,” Ph. D. Dissertation, Department of Computer Science, Stanford University, Stanford, California (Aug. 1978).

    Google Scholar 

  12. J. Valdes, R. E. Tarjan and E. L. Lawler, “The recognization of series parallel digraphs,”Proceedings of the Eleventh Annual Symposium on the Theory of Computing (1979), pp. 1–12.

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Authors and Affiliations

  1. Department of Computer Science, University of Kentucky, Lexington, Kentucky

    Johnson M. Hart

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  1. Johnson M. Hart
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Hart, J.M. Fast recognition of Baxter permutations using syntactical and complete bipartite composite dag's. International Journal of Computer and Information Sciences 9, 307–321 (1980). https://doi.org/10.1007/BF00978163

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  • DOI: https://doi.org/10.1007/BF00978163

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