Faces and Bases: Dehn-sommerville Type Relations
نویسنده
چکیده
We review several linear algebraic aspects of the DehnSommerville relations and relate redundant analogues of the f and h-vectors describing the subsets of a simplex 2 that satisfy Dehn-Sommerville type relations to integer points contained in some rational polytopes.
منابع مشابه
8 Applications of Klee ’ s Dehn - Sommerville relations
We use Klee’s Dehn-Sommerville relations and other results on face numbers of homology manifolds without boundary to (i) prove Kalai’s conjecture providing lower bounds on the f -vectors of an even-dimensional manifold with all but the middle Betti number vanishing, (ii) verify Kühnel’s conjecture that gives an upper bound on the middle Betti number of a 2k-dimensional manifold in terms of k an...
متن کاملApplications of Klee's Dehn-Sommerville Relations
We use Klee’s Dehn-Sommerville relations and other results on face numbers of homology manifolds without boundary to (i) prove Kalai’s conjecture providing lower bounds on the f -vectors of an even-dimensional manifold with all but the middle Betti number vanishing, (ii) verify Kühnel’s conjecture that gives an upper bound on the middle Betti number of a 2k-dimensional manifold in terms of k an...
متن کاملCombinatorial Hopf Algebras and Generalized Dehn-sommerville Relations
A combinatorial Hopf algebra is a graded connected Hopf algebra over a field k equipped with a character (multiplicative linear functional) ζ : H → k. We show that the terminal object in the category of combinatorial Hopf algebras is the algebra QSym of quasi-symmetric functions; this explains the ubiquity of quasi-symmetric functions as generating functions in combinatorics. We illustrate this...
متن کاملAn Euler Relation for Valuations on Polytopes
A locally finite point set (such as the set Z of integral points) gives rise to a lattice of polytopes in Euclidean space taking vertices from the given point set. We develop the combinatorial structure of this polytope lattice and derive Euler-type relations for valuations on polytopes using the language of Mo bius inversion. In this context a new family of inversion relations is obtained, the...
متن کاملGenocchi numbers and f-vectors of simplicial balls
The aim of this note is to investigate f -vectors of simplicial balls, especially the relations between interior and boundary faces. For a simplicial ball B we denote by fi(B) the number of i-dimensional faces. The boundary ∂B of B is a simplicial sphere with face numbers fi(∂B). We also define fi(int B) := fi(B) − fi(∂B) although the interior int B of B is not a polyhedral complex. For simplic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004