Some bijective results about the ares of Schröder paths

  • Authors:

  • L. Ferrari;E. Grazzini;E. Pergola;S. Rinaldi

  • Affiliations:

  • Dipartimento di Matematica "U. Dini", Viale Morgagni 67/A, 50134 Firenze, Italy;Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Matematica "R. Magari", via del Capitano 15, 53100 Siena, Italy

  • Venue:
  • Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
  • Year:
  • 2003

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Abstract

In the existing literature there are many combinatorial interpretations for the sequence (ai)i≥1 = 1,3,7,17,41,... (M2665 in The Encyclopedia of Integer Sequences, Academic Press, New York, 1995), and at least one for the subsequence of its odd-indexed terms, i.e. 1,7,41,239,..., using the area under elevated Schröder paths. We provide a combinatorial interpretation for the subsequence given by the remaining terms 3,17,99,..., also in this case by using the area under Schröder paths.