Some combinatorial properties of hexagonal lattices
In this paper, we consider the combinatorial properties of the hexagonal lattice. Let $e(n)$ be the number of $n$-element order ideals in a hexagonal lattice. We give the enumeration of $e(n)$ by showing a bijection between the order ideals and Schröder paths. Further, we get formulae for the flag $f$- and $h$-vectors of the hexagonal lattice.
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