Beyond Simplices: Thinking outside the Simplex; but Not Too Far
نویسندگان
چکیده
1. Write-up Wish List 2 2. To Do List 2 3. History 3 4. Basic definitions and notation 4 5. Codimension One Finite Length [Sarah] 5 6. Codimension Two Finite Length [Sarah] 5 7. Codimension Three Finite Length 7 8. Attempts at Codimension Four 8 9. Betti Death 8 10. Alternative diagram decompostions for complete intersections 9 11. Decomposition Via Separating the Betti Diagram 13 11.1. Heuristic Separation Procedure 13 11.2. Separating Diagrams 14 12. Tensor products of diagrams 15 13. Acknowledgements 18 References 18 Appendix A. Toij’s: A collections of fun code we have written 18
منابع مشابه
Möbius Pairs of Simplices and Commuting Pauli Operators
There exists a large class of groups of operators acting on Hilbert spaces, where commutativity of group elements can be expressed in the geometric language of symplectic polar spaces embedded in the projective spaces PG(n, p), n being odd and p a prime. Here, we present a result about commuting and non-commuting group elements based on the existence of socalled Möbius pairs of n-simplices, i. ...
متن کاملSimplicial Complexes: Second Lecture
Suppose that K and L are simplicial complexes. Recall that a vertex map between these complexes is a function φ : V ert(K) → V ert(L) such that the vertices of a simplex in K map to the vertices of a simplex in L. Given such a φ, we can create a simplicial map f : |K| → |L| by linearly extending φ over each simplex. On the other hand, suppose we have an arbitrary continuous map g : |K| → |L|. T...
متن کاملGeometry of carrying simplices of 3-species competitive Lotka-Volterra systems
We investigate the existence, uniqueness and Gaussian curvature of the invariant carrying simplices of 3 species autonomous totally competitive Lotka-Volterra systems. Explicit examples are given where the carrying simplex is convex or concave, but also where the curvature is not single-signed. Our method monitors the curvature of an evolving surface that converges uniformly to the carrying sim...
متن کاملCombinatorial models for topology-based geometric modeling
simplicial complexes (ASCs) are one of the most known topological models [1, 89, 21, 32]. Semi-simplicial sets (SSSs) generalize them [82, 67, 68], i.e. a SSS can be associated with any ASC, but the converse is not true. In particular, SSSs can represent « curved » objects, maybe multi-incident, but it is not possible for ASCs. The definition type also differs: ASCs are sets of sets, SSSs are a...
متن کاملLARGEST j-SIMPLICES IN d-CUBES: SOME RELATIVES OF THE HADAMARD MAXIMUM DETERMINANT PROBLEM
This paper studies the computationally diicult problem of nding a largest j-dimensional simplex in a given d-dimensional cube. The case in which j = d is of special interest, for it is equivalent to the Hadamard maximum determinant problem; it has been solved for innnitely many values of d but not for d = 14. (The subcase in which j = d 3 (mod 4) subsumes the famous problem on the existence of ...
متن کامل