Geodesic
Dynkin diagram classification of $\lambda$-minuscule Bruhat lattices and of $d$-complete posets
Journal of Algebraic Combinatorics, Tome 9 (1999) no. 1, pp. 61-94.

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Summary: d-Complete posets are defined to be posets which satisfy certain local structural conditions. These posets play or conjecturally play several roles in algebraic combinatorics related to the notions of shapes, shifted shapes, plane partitions, and hook length posets. They also play several roles in Lie theory and algebraic geometry related to $lambda$-minuscule elements and Bruhat distributive lattices for simply laced general Weyl or Coxeter groups, and to $lambda$-minuscule Schubert varieties. This paper presents a classification of d-complete posets which is indexed by Dynkin diagrams.
Keywords: d-complete poset, minuscule Weyl group element, reduced decomposition, Dynkin diagram 
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     title = {Dynkin diagram classification of $\lambda$-minuscule {Bruhat} lattices and of $d$-complete posets},
     journal = {Journal of Algebraic Combinatorics},
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Proctor, Robert A. Dynkin diagram classification of $\lambda$-minuscule Bruhat lattices and of $d$-complete posets. Journal of Algebraic Combinatorics, Tome 9 (1999) no. 1, pp. 61-94. http://geodesic.mathdoc.fr/item/JAC_1999__9_1_a0/