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We study the commutative algebras $Z_{JK}$ appearing in Brown and Goodearls extension of the $mathcal{H}$-stratification framework, and show that if $A$ is the single parameter quantized coordinate ring of $M_{m,n}$, $GL_n$ or $SL_n$, then the algebras $Z_{JK}$ can always be constructed in terms of centres of localizations. The main purpose of the $Z_{JK}$ is to study the structure of the topological space $spec(A)$, which remains unknown for all but a few low-dimensional examples. We explicitly construct the required denominator sets using two different techniques (restricted permutations and Grassmann necklaces) and show that we obtain the same sets in both cases. As a corollary, we obtain a simple formula for the Grassmann necklace associated to a cell of totally nonnegative real $mtimes n$ matrices in terms of its restricted permutation.
We prove that an inverse-free equation is valid in the variety LG of lattice-ordered groups (l-groups) if and only if it is valid in the variety DLM of distributive lattice-ordered monoids (distributive l-monoids). This contrasts with the fact that,
This paper studies new properties of the front and back ends of a sorting network, and illustrates the utility of these in the search for new bounds on optimal sorting networks. Search focuses first on the outsides of the network and then on the inne
While the beginning decade of the high-Tc cuprates era passed under domination of local theories, Abrikosov was one of the few who took seriously the electronic band structure of cuprates, stressing the importance of an extended Van Hove singularity
The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron $mathcal{M}_{n,k}
We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium correspond