Why is this lattice modular?

96 Views Asked by At

I'm reading Stanley's Enumerative Combinatorics, and he says every lattice with at most six elements is modular. But what about the lattice below on the right? If $x,y$ are the two elements at the penultimate level, it seems $x\vee y :> x,y$ but $x \wedge y \not<: x,y$. What am I missing?

lattices

Edit: Never mind, he said every semimodular lattice with $\leq 6$ elements is modular.

1

There are 1 best solutions below

0
On BEST ANSWER

Providing a target to accept the answer, as the OP has answered his own question.

Edit: Never mind, he said every semimodular lattice with $\ge 6$ elements is modular.