2019/11/25 by I. Tasoulas, Tasoulas, I., K. Manes +5
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1911.10883
We call an interval [x,y] in a poset \em 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.