P. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom., 15 (1996), pp. 307--340. Home/Search Document Not in Database Summary Related Articles Check |
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A Theorem on Higher Bruhat Orders - Felsner, Weil (1998) (Correct)
....of pseudolines, higher Bruhat order. 1 Preliminaries Higher Bruhat orders were introduced by Manin and Schechtman [5] as generalizations of the weak Bruhat order on the symmetric group S n . Further investigations of the subject are Voevodskij and Kapranov [6] Ziegler [7] Edelman and Reiner [1, 2] and Felsner and Weil [3] Let us review the definition. The set [n] f1; ng is equipped with the natural linear order. The set of s element subsets of [n] is . For X 2 with s i 1 we let X denote the set X minus the ith largest element of X (e.g. f3; 5; 8; 9g = f3; 8; ....
P. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom., 15 (1996), pp. 307--340.
Piles Of Cubes, Monotone Path Polytopes And Hyperplane.. - Athanasiadis (Correct)
....interpretation [2, Thm. 8.2.1] We don t know if a fiber polytope construction for the polar complexes exists in this case. 5. The cones of the extended Catalan arrangements A [0;a] d were shown to be inductively free [10, Ch. 4] by Edelman and Reiner (see the proof of Theorem 3. 2 in [9]) Other classes of deformations of A d , including the extended Shi arrangements, were shown to be inductively free in [3] Proposition 4.2 suggests that the same is true for the arrangements A d ( Acknowledgement. I am grateful to Lou Billera and Bernd Sturmfels for helpful discussions. ....
P.H. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom. 15 (1996), 307--340.
On Free Deformations of the Braid Arrangement - Athanasiadis (1997) (1 citation) (Correct)
....the root systems A n Gamma1 and B n were studied by J ozefiak and Sagan [9] These arrangements can also be related to graphs. Edelman and Reiner [5] gave a complete classification of the free arrangements in this case and showed that they correspond to threshold graphs. In more recent work [6] these authors classified the free arrangements which arise as discriminantal arrangements of two dimensional zonotopes with integer side lengths. We will be concerned with deformations of A n . The combinatorics of such arrangements was first studied in a systematic way by Stanley and ....
....by Headley [7, 8] This agrees with Shi s result [13] that it divides R n into (n 1) n Gamma1 regions. A simple counting proof of Headley s result, based on the finite field method, was given in [1, 2] Freeness of the associated homogenized linear arrangement, or cone, was conjectured in [6]. Our motivation comes primarily from [1, 2] In this work the characteristic polynomials of large classes of deformations of Coxeter arrangements were shown to factor completely over the nonnegative integers and the question of freeness of their cones was naturally raised [1, x7] 2, x8.4] Our ....
[Article contains additional citation context not shown here]
P.H. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom. 15 (1996), 307--340.
A Theorem on Higher Bruhat Orders - Felsner, Weil (1998) (Correct)
....of pseudolines, higher Bruhat order. 1 Preliminaries Higher Bruhat orders were introduced by Manin and Schechtman [5] as generalizations of the weak Bruhat order on the symmetric group S n . Further investigations of the subject are Voevodskij and Kapranov [6] Ziegler [7] Edelman and Reiner [1, 2] and Felsner and Weil [3] Let us review the definition. The set [n] f1; ng is equipped with the natural linear order. The set of s element subsets of [n] is Gamma [n] s Delta . For X 2 Gamma [n] s Delta with s i 1 we let X bic denote the set X minus the ith largest ....
P. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom., 15 (1996), pp. 307--340.
Piles Of Cubes, Monotone Path Polytopes And Hyperplane.. - Athanasiadis (1997) (Correct)
....interpretation [2, Thm. 8.2.1] We don t know if a fiber polytope construction for the polar complexes exists in this case. 5. The cones of the extended Catalan arrangements A [0;a] d were shown to be inductively free [9, Ch. 4] by Edelman and Reiner (see the proof of Theorem 3. 2 in [8]) Other classes of deformations of A d , including the extended Shi arrangements, were shown to be inductively free in [3] Proposition 4.2 suggests that the same is true for the arrangements A d ( Acknowledgement. I am grateful to Lou Billera and Bernd Sturmfels for helpful discussions. ....
P. H. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom. 15 (1996), 307--340.
Deformations of Coxeter Hyperplane Arrangements - Postnikov, Stanley (2000) (14 citations) (Correct)
No context found.
P. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom. 15 (1996), 307-340.
Deformations of Coxeter Hyperplane Arrangements - Postnikov, Stanley (2000) (14 citations) (Correct)
No context found.
P. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom. 15 (1996), 307#340.
A Simple Bijection For The Regions Of The Shi Arrangement .. - Athanasiadis, Linusson (4 citations) (Correct)
No context found.
P.H. Edelman and V. Reiner, Free arrangements and rhombic tilings, Discrete Comput. Geom. 15 (1996), 307--340.
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