Hyperfactord of Shi arrangement Sh(A2) and Sh(A3)

Authors

  • Alaa A. A. Al-Mujmaey Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, IRAQ.
  • Rabeaa G. A. Al-Aleyawee Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, IRAQ.

DOI:

https://doi.org/10.23851/mjs.v33i3.1139

Keywords:

Hyperplane arrangement, Briad arrangement, Shi arrangement.

Abstract

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.

 

 

 

References

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.‏‏‏

CrossRef DOI: https://doi.org/10.1007/BFb0074969

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.

CrossRef DOI: https://doi.org/10.1023/A:1008717901994

Rhoades, B., & Armstrong, D. The Shi arrangement and the Ish arrangement. Discrete Mathematics & Theoretical Computer Science, 2011.‏

CrossRef DOI: https://doi.org/10.46298/dmtcs.2890

Fishel, S. A survey of the Shi arrangement. In Recent Trends in Algebraic Combinatorics (pp. 75-113). Springer, Cham, 2019.‏

CrossRef DOI: https://doi.org/10.1007/978-3-030-05141-9_3

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.

CrossRef DOI: https://doi.org/10.1006/jcta.1997.2793

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.

CrossRef DOI: https://doi.org/10.4153/CJM-1960-055-3

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Published

2022-09-25

How to Cite

[1]
A. A. A. Al-Mujmaey and R. G. A. . Al-Aleyawee, “Hyperfactord of Shi arrangement Sh(A2) and Sh(A3)”, Al-Mustansiriyah Journal of Science, vol. 33, no. 3, pp. 43–47, Sep. 2022.

Issue

Section

Mathematics