Titlebook: Combinatorial Methods in Topology and Algebra; Bruno Benedetti,Emanuele Delucchi,Luca Moci Book 2015 Springer International Publishing Swi

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M. Clincy,H. S. Bond,S. Whitelamf groups parametrizes all quotients of the complex reflection groups .(.,?.,?.) by scalar subgroups. Our classification is ultimately incomplete, but we provide several necessary and sufficient conditions for generalized involution models to exist in various cases. In the process we have been led to

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A. B. Egorova,N. Hoshi,H. Higashidashort proof of this result, along with a broad generalization to matrices with multi-homogeneous structures. Our main tool is a rigidity statement for radical Borel-fixed ideals in multigraded polynomial rings. For a more detailed exposition of the matter of this chapter we refer to the paper “Unive

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Slow Synaptic Responses and Modulationaper (Denham and Suciu, Proc. Lond. Math. Soc. .(6), 1435–1470, 2014), the homology groups of the Milnor fiber of such an arrangement can have non-trivial integer torsion. We give here a brief account of the techniques that go into proving this result, outline some of its applications, and indicate

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Norberto Patrignani,Diane Whitehouse projective resolutions of high powers is rather non-trivial if the ideals aren’t particularly well behaved. We describe how the asymptotic decomposition of Betti tables of high powers can be conjecturally described using polytopes as a new invariant for the stable regime.

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Subacute Sclerosing Panencephalitiss shows that not every triangulation of a sphere, where angles around faces of codimension two are less than 2. in the metric pieced together by regular Euclidean simplices, is polytopal. The counterexample presented here is the smallest triangulation of . where every edge is contained in an empty t

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https://doi.org/10.1007/978-1-4612-9883-0 properties of the types of points in an arrangement of tropical hyperplanes—in much the same way as the covectors of (classical) oriented matroids describe the types in arrangements of linear hyperplanes.They are in correspondence with other objects of interest in discrete geometry: subdivisions of

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Volker ter Meulen M.D.,Michael Katz M.D. representable matroids using Milnor numbers and the Bergman fan. The same approach to the conjecture in the general case (for possibly non-representable matroids) leads to several intriguing questions on higher codimension algebraic cycles in toric varieties.

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