2014
DOI: 10.1080/00927872.2013.865051
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A Basis Construction for the Shi Arrangement of the TypeBorC

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Cited by 5 publications
(4 citation statements)
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“…First, in [19], a basis for D(c Shi (1)) was constructed using the Bernoulli polynomial. Subsequently, in [10] and [18], similar bases were constructed for root systems of type B, C, and D. Note that these works are for Shi arrangements with m = 1. Catalan arrangements and Shi arrangements with m > 1 have not been covered.…”
Section: Constructions Of Explicit Basesmentioning
confidence: 99%
“…First, in [19], a basis for D(c Shi (1)) was constructed using the Bernoulli polynomial. Subsequently, in [10] and [18], similar bases were constructed for root systems of type B, C, and D. Note that these works are for Shi arrangements with m = 1. Catalan arrangements and Shi arrangements with m > 1 have not been covered.…”
Section: Constructions Of Explicit Basesmentioning
confidence: 99%
“…First, in [18], a basis for D(c Shi ℓ (1)) was constructed using the Bernoulli polynomial. Subsequently, in [10] and [19], similar bases were constructed for root systems of type B, C, and D. Note that these works are for Shi arrangements with m = 1. Catalan arrangements and Shi arrangements with m > 1 have not been covered.…”
mentioning
confidence: 99%
“…However, there have been few researches how to construct their explicit bases. Recently, in the case of types A ℓ , B ℓ , C ℓ , D ℓ , explicit bases for the cone cShi 1 over the Shi arrangements were constructed ( [7], [8], [3]). Also, a nice basis for the extended Shi arrangements was determined in [2].…”
mentioning
confidence: 99%