5 citations · 11 across the 11 of their papers we have counts for
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The Cohen-Macaulayness of the bounded complex of an affine oriented matroid
Ryota Okazaki, Kohji Yanagawa
An affine oriented matroid is a combinatorial abstraction of an affine hyperplane arrangement. From it, Novik, Postnikov and Sturmfels constructed a squarefree monomial ideal in a…
On CW complexes supporting Eliahou-Kervaire type resolutions of Borel fixed ideals
Ryota Okazaki, Kohji Yanagawa
We prove that the Eliahou-Kervaire resolution of a Cohen-Macaulay stable monomial is supported by a regular CW complex whose underlying space is a closed ball. We also show that th…
On the radical of multigraded modules
Viviana Ene, Ryota Okazaki
We define a functor $\rr^\ast$ from the category of positively determined modules to the category of squarefree modules which plays the role of passing from a monomial ideal to its…
Toric rings arising from cyclic polytopes
Takayuki Hibi, Akihiro Higashitani, Lukas Katth"an +1
In the present paper, we consider the problem when the toric ring arising from an integral cyclic polytope is Cohen-Macaulay by discussing Serre's condition and we give a complete…
Alternative polarizations of Borel fixed ideals, Eliahou-Kervaire type resolution and discrete Morse theory
Ryota Okazaki, Kohji Yanagawa
We construct an Eliahou-Kervaire-like minimal free resolution of the alternative polarization of a Borel fixed ideal . It yields new descriptions of the minimal free…
Alexander duality and Stanley depth of multigraded modules
Ryota Okazaki, Kohji Yanagawa
We apply Miller's theory on multigraded modules over a polynomial ring to the study of the Stanley depth of these modules. Several tools for Stanley's conjecture are developed, and…