On the Freeness of 3‐Arrangements

By Masahiko Yoshinaga. 2005

93 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/52b1697483aa45378b2d2fcf8845fd6830eb8733

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Takuro Abe
2. Stefan O. Tohaneanu
3. Aron Simis
4. Max Wakefield
5. Hiroaki Terao
6. Masahiko Yoshinaga
7. Seyed Hamid Hassanzadeh

In Discrete Mathematics and Combinatorics

1. Takuro Abe
2. Masahiko Yoshinaga
3. Max Wakefield
4. Hiroaki Terao
5. Stefan O. Tohaneanu
6. Aron Simis
7. Nicholas Proudfoot
8. David E. Speyer

In Electrical and Electronic Engineering

1. Takuro Abe
2. Stefan O. Tohaneanu
3. Aron Simis
4. Max Wakefield
5. Hiroaki Terao
6. Masahiko Yoshinaga

Citations in the corpus

• Plus-one Generated and Next to Free Arrangements of Hyperplanes (2018, background): “Saito in [17], or Yoshinaga in [21], [22], [10].”
• Characterization of a free arrangement and conjecture of Edelman and Reiner (2004, unknown): “For a rank two root system, the conjecture has been already verified [ Yo ].”
• Homology of homogeneous divisors (2012, background): “When Y is a hyperplane arrangement in a vector space of finite dimension, free divisors received a great deal of interest: [19, 22, 24, 29, 30, 34] to cite just a few.”
• Freeness of hyperplane arrangements and related topics (2012, background): “for ℓ = 3, both conditions are automatically satisfied, however, there exist non free 3- arrangements. For characterizing freeness of 3-arrangements, we need characteristic polynomials. Theorem 1.39. ([48]) Let A be a 3-arrangement. Set χ(A,t) = (t − 1)(t2 − b 1t+b2) and exp(AH1,mH1) = (d1,d2). Then ”
• THE CHARACTERISTIC POLYNOMIAL OF A MULTIARRANGEMENT (2006, background): “Later in [14] and [15] Yoshinaga found that the derivation modules of multiarrangements are important for the study of free arrangements.”
• Divisionally free arrangements of hyperplanes (2015, background): “y of free arrangements was initiated by Terao in [19], and has been playing the central role in this area. Recently, there have been several studies to determine when A is free, e.g., [2], [9], [21], [22] and so on. However, it is still very difficult to determine the freeness. Freeness of arrangement”