Chains with Small Intervals in the Lattice of Binary Paths
I. Tasoulas, K. Manes, A. Sapounakis, and P. Tsikouras
Department of Informatics
University of Piraeus
We call an interval [x, y] in a poset
small if y is the join of some
elements covering x. In this paper, we study the chains of paths from a
given arbitrary (binary) path P to the maximum path having only small
intervals. More precisely, we obtain and use several formulas for the
enumeration of chains having only small intervals and minimal length. For
this, we introduce and study the notions of filling and degree of a path,
giving in addition some related statistics.
Full version: pdf,
(Concerned with sequences
Received May 8 2019; revised versions received August 29 2019; September 27 2019.
Published in Journal of Integer Sequences,
December 29 2019.
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