Journal of Integer Sequences, Vol. 23 (2020), Article 20.1.5

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
18534 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.

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(Concerned with sequences A000108 A000213 A001405.)

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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