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Combinatorial Properties of the Antichains of a Garland

Veröffentlicht/Copyright: 31. August 2009
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Abstract

In this paper we study some combinatorial properties of the antichains of a garland, or double fence (see Figure 1 for an example). Specifically, we encode the order ideals and the antichains in terms of words of a regular language, we obtain several enumerative properties (such as generating series, recurrences and explicit formulae), we consider some statistics leading to Riordan matrices, we study the relations between the lattice of ideals and the semilattice of antichains, and finally we give a combinatorial interpretation of the antichains as lattice paths with no peaks and no valleys.

Keywords.: Double fences; order ideals; Chebyshev polynomials; trinomial paths; Motzkin paths; enumeration; formal series
Received: 2008-05-16
Revised: 2009-02-24
Accepted: 2009-03-05
Published Online: 2009-08-31
Published in Print: 2009-September

© de Gruyter 2009

Artikel in diesem Heft

  1. On Relatively Prime Sets
  2. Combinatorial Properties of the Antichains of a Garland
  3. φ(Fn) = Fm
  4. Twelfth Power Qualified Residue Difference Sets
  5. On Pebbling Graphs by Their Blocks
  6. Conjugacy Classes and Class Number
  7. Infinite Families of Divisibility Properties Modulo 4 for Non-Squashing Partitions into Distinct Parts
  8. Waring's Number in a Finite Field
  9. Lucas Diophantine Triples
https://doi.org/10.1515/INTEG.2009.030
Schlagwörter für diesen Artikel
Double fences; order ideals; Chebyshev polynomials; trinomial paths; Motzkin paths; enumeration; formal series

Artikel in diesem Heft

  1. On Relatively Prime Sets
  2. Combinatorial Properties of the Antichains of a Garland
  3. φ(Fn) = Fm
  4. Twelfth Power Qualified Residue Difference Sets
  5. On Pebbling Graphs by Their Blocks
  6. Conjugacy Classes and Class Number
  7. Infinite Families of Divisibility Properties Modulo 4 for Non-Squashing Partitions into Distinct Parts
  8. Waring's Number in a Finite Field
  9. Lucas Diophantine Triples
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