The cubicald-polytopes with fewer than 2 d+1 vertices
نویسندگان
چکیده
منابع مشابه
There Are Asymptotically Far Fewer Polytopes than We Thought
The problem of enumerating convex polytopes with n vertices in R has been the object of considerable study going back to ancient times (see [4, §13.6] for some remarks about the history of this problem since the nineteenth century). While significant progress has been made when the number of vertices was not too much larger than the dimension [4], little had been known above dimension 3 in the ...
متن کاملCounting d-Polytopes with d+3 Vertices
We completely solve the problem of enumerating combinatorially inequivalent d-dimensional polytopes with d + 3 vertices. A first solution of this problem, by Lloyd, was published in 1970. But the obtained counting formula was not correct, as pointed out in the new edition of Grünbaum’s book. We both correct the mistake of Lloyd and propose a more detailed and self-contained solution, relying on...
متن کاملOn Vertices and Facets of Combinatorial 2-Level Polytopes
2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arising in combinatorial settings. Our first contribution is proving that f0(P )fd−1(P ) ≤ d2 for a large collection of families of such polytopes...
متن کاملVertices of Gelfand-Tsetlin Polytopes
This paper is a study of the polyhedral geometry of Gelfand–Tsetlin polytopes arising in the representation theory of glnC and algebraic combinatorics. We present a combinatorial characterization of the vertices and a method to calculate the dimension of the lowest-dimensional face containing a given Gelfand–Tsetlin pattern. As an application, we disprove a conjecture of Berenstein and Kirillov...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1995
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02574048