Chains with small intervals in the lattice of binary paths
I Tasoulas, K Manes, A Sapounakis… - arXiv preprint arXiv …, 2019 - arxiv.org
arXiv preprint arXiv:1911.10883, 2019•arxiv.org
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.
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.
We call an interval in a poset {\em small} if is the join of some elements covering . In this paper, we study the chains of paths from a given arbitrary (binary) path 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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