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We will using the combinatorics of the G-stable pieces to describe the closure relation of the partition of partial flag varieties in [L3, section 3]. 1. Some combinatorics 1.1. Let k be an algebraic closure of the finite field Fq and G be a connected reductive algebraic group defined over Fq with Frobenius map F : G → G. We fix a F -stable Borel subgroup B of G and a F -stable maximal torus T ⊂ B. Let I be the set of simple roots determined by B and T . Then F induces an automorphism on the Weyl group W which we deonte by δ. The autmorphism restricts to a bijection on the set I of simple roots. By abusion notations, we also denote the bijection by δ. For any J ⊂ I, let PJ be the standard parabolic subgroup corresponding to J and PJ be the set of parabolic subgroups that are G-conjugate to PJ . We simply write P∅ as B. Let LJ be the Levi subgroup of PJ that contains T . For any parabolic subgroup P , let UP be the unipotent radical of P . We simply write U for UB. For J ⊂ I, we denote by WJ the standard parabolic subgroup of W generated by J and by W J (resp. W ) the set of minimal coset representatives in W/WJ (resp. WJ\W ). For J,K ⊂ I, we simply write W J ∩ W as W J . For P ∈ PJ and Q ∈ PK , we write pos(P,Q) = w if w ∈ W and there exists g ∈ G such that P = gPJg, Q = gẇPKẇg, where ẇ is a representative of w in N(T ). For g ∈ G and H ⊂ G, we write H for gHg. We first recall some combinatorial results. 1.2. For J ⊂ I, let T (J, δ) be the set of sequences (Jn, wn)n≥0 such that (a) J0 = J , (b) Jn = Jn−1 ∩Ad(wn−1)δ(Jn−1) for n ≥ 1, (c) wn ∈ nW δ(Jn) for n ≥ 0, (d) wn ∈ WJnwn−1Wδ(Jn−1) for n ≥ 1. 2000 Mathematics Subject Classification. 14M15, 20G40. The author is partially supported by NSF grant DMS-0700589.