Abstract
Recall that a partially ordered set L is a geometric lattice if
-
(a)
it has a unique minimal element, 0
-
(b)
for each v∈Lall maximally ordered chains 0 = v0<v1<…<vp = v have the same number of elements, in which case we say the rank of v is p and we write p = r(v).
-
(c)
This function satisfies
$$ r(v \wedge w) + r(v \vee w) \leqslant r(v) + r(w) $$ -
(d)
every element is a join of elements of rank 1
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© 1988 Springer-Verlag Berlin Heidelberg
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Goresky, M., MacPherson, R. (1988). Proofs of Theorems B, C, and D. In: Stratified Morse Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71714-7_28
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DOI: https://doi.org/10.1007/978-3-642-71714-7_28
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