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Rouquier dimension is Krull dimension for normal toric varieties
We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull...
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Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws
In this paper, we propose a finite volume Hermite weighted essentially non-oscillatory (HWENO) method based on the dimension by dimension framework...
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Dimension of non-summand submodules
We introduce and study the concept of essential Krull dimension as dual of small Krull dimension of a module, which are defined in the same vein as...
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Mean dimension of continuous cellular automata
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean...
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Die vierte Dimension
Wir beschreiben einen vierdimensionalen Ort, das heißt, einen Teil eines vierdimensionalen Raums, der von einem Hyperwürfel eingeschlossen ist....
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On the dynamic asymptotic dimension of étale groupoids
We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several...
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The shift-dimension of multipersistence modules
We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of...
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Dimension theory of Lüroth digits
We investigate the relative growth properties of the Lüroth digits and establish the Hausdorff dimension of exceptional sets of points with a given...
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Polynomial growth and asymptotic dimension
Bonamy et al. [4] showed that graphs of polynomial growth have finite asymptotic dimension. We refine their result showing that a graph of polynomial...
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Relative entropy dimension for countable amenable group actions
We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups. First, for a given Følner...
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Dimension of a Graph
In 1965, a distinguished group of mathematicians consisting of Paul Erdős, Frank Harary, and William Thomas Tutte created a notion of the dimension...
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A Fubini-type theorem for Hausdorff dimension
It is well known that a classical Fubini theorem for Hausdorff dimension cannot hold; that is, the dimension of the intersections of a fixed set with...
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A reasonable notion of dimension for singular intersection homology
M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula...
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A Note on the Global Dimension of Shifted Orders
We consider the dominant dimension of an order over a Cohen-Macaulay ring in the category of centrally Cohen-Macaulay modules. There is a canonical...
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Genericity of Homeomorphisms with Full Mean Hausdorff Dimension
It is well known that the presence of horseshoes leads to positive entropy. If our goal is to construct a continuous map with infinite entropy, we...
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On Variational Principles of Metric Mean Dimension on Subsets in Feldman–Katok Metric
In this paper, we studied the metric mean dimension in Feldman–Katok (FK for short) metric. We introduced the notions of FK-Bowen metric mean...
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Metric Mean Dimension of Free Semigroup Actions for Non-Compact Sets
In this paper, we introduce the notions of upper metric mean dimension, u -upper metric mean dimension, l -upper metric mean dimension of free...
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Modules with finite reducing Gorenstein dimension
If M is a nonzero finitely generated module over a commutative Noetherian local ring R such that M has finite injective dimension and finite...