Related papers: Faces and bases: Dehn-Sommerville type relations

This text is the English translation of a 1986 manuscript which gives the classification of the differential forms parametrizing the finite-dimensional Lie algebras of hamiltonian and contact Cartan types over fields of positive…

A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra $\cal G$ is considered. The solution contains a metric, $n$ Abelian 2-forms and $n$ scalar fields, where $n$ is the rank of $\cal G$. It is governed by a…

We prove that if a pure simplicial complex of dimension d with n facets has the least possible number of (d-1)-dimensional faces among all complexes with n faces of dimension d, then it is vertex decomposable. This answers a question of J.…

Generalized composite fluxbrane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold which contains a product of n Ricci-flat spaces M_1 x ... x M_n with 1-dimensional M_1. They are defined…

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…

We study the homotopy type of the simplicial set of continuous semi-algebraic simplexes of an algebraic variety defined over a real closed field, which we will call the real homotopy type. We prove an analogue of the theorem of Artin-Mazur…

We give explicit polynomial-sized (in $n$ and $k$) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree $k$ in $n$ variables. These convex cones form a family of…

Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral…

The paper contains integral representations for certain classes of exponentially growing solutions of second order periodic elliptic equations. These representations are the analogs of those previously obtained by S. Agmon, S. Helgason, and…

The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces…

Hecke symmetries generalize the usual tensor symmetry of vector spaces $v\otimes w\arrow w\otimes v$ as well as the symmetry of vector superspaces. To a Hecke symmetry $R$ there associates a quadratic algebra which can be interpreted as the…

Equifacetal simplices, all of whose codimension one faces are congruent to one another, are studied. It is shown that the isometry group of such a simplex acts transitively on its set of vertices, and, as an application, equifacetal…

Polytope numbers for a given polytope are an integer sequence defined by the combinatorics of the polytope. Recent work by H. K. Kim and J. Y. Lee has focused on writing polytope number sequences as sums of simplex number sequences. In…

We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…

Let X be a smooth hypersurface in projective space. We discuss in this paper when X can be defined by an equation det M = 0 (resp. pf M = 0), where M is a matrix (resp. a skew-symmetric matrix) with homogeneous entries. Standard homological…

For a $d$-dimensional polytope with $v$ vertices, $d+1\le v\le2d$, we calculate precisely the minimum possible number of $m$-dimensional faces, when $m=1$ or $m\ge0.62d$. This confirms a conjecture of Gr\"unbaum, for these values of $m$.…

For a symmetric 2t-cycle in the tope graph of a simple oriented matroid M on the ground set {1,...,t}, where t is even, we describe decompositions of topes and subtopes of M with respect to the subtopes corresponding to the edges of the…

Let X,Y be finite sets and T a set of functions from X -> Y which we will call "tableaux". We define a simplicial complex whose facets, all of the same dimension, correspond to these tableaux. Such "tableau complexes" have many nice…

We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials to the non-commutative setting. We then solve linear…

Let $\Delta$ be a Delzant polytope in ${\mathbb R}^n$ and ${\mathbf b}\in{\mathbb Z}^n$. Let $E$ denote the symplectic fibration over $S^2$ determined by the pair $(\Delta,\,{\mathbf b})$. Under certain hypotheses, we prove the equivalence…