Hyperfactord of Shi arrangement Sh(A2) and Sh(A3)
Keywords:Hyperplane arrangement, Briad arrangement, Shi arrangement.
In this paper, we introduce the region and the faces poset of shi arrangement that J. Y. Shi firstly introduced it. This is an affine arrangement, each of whose hyperplane is parallel to some"hyperplane of Coxeter arrangement"(Braid arrangement), the degrees and the exponents of this arrangement were found and we prove the shi arrangement is ahyperfactored arrangement when n=3 and not hyperfactored arrangement when n=4 arrangement.
Stanley, R. P. An introduction to hyperplane arrangements. Geometric combinatorics, 13(389-496), 24, 2004.
Shi, J. Y. The Kazhdan-Lusztig cells in certain affine Weyl groups. Lecture notes in Mathematics, 1179, 1-307, 1986.
Abebe, R. Counting regions in hyperplane arrangements. Harvard College Math Review, 5.
Rincón, F. A Labelling of the Faces in the Shi Arrangement. Rose-Hulman Undergraduate Mathematics Journal, 8(1), 7. 2007.
Denham, G. Hanlon and Stanley's conjecture and the Milnor fibre of a braid arrangement. Journal of Algebraic Combinatorics, 11(3), 227-240, 2000.
Rhoades, B., & Armstrong, D. The Shi arrangement and the Ish arrangement. Discrete Mathematics & Theoretical Computer Science, 2011.
Fishel, S. A survey of the Shi arrangement. In Recent Trends in Algebraic Combinatorics (pp. 75-113). Springer, Cham, 2019.
Athanasiadis, C. A. A class of labeled posets and the Shi arrangement of hyperplanes. Journal of combinatorial theory, Series A, 80(1), 158-162,1997.
Levear, D. A bijection for Shi arrangement faces,2019.
Steinberg, R. (1960). Invariants of finite reflection groups. Canadian Journal of Mathematics, 12, 616-618, 1960.
How to Cite
Copyright (c) 2022 Al-Mustansiriyah Journal of Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC-BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.