Related papers: The Poincar\'e-extended ab-index
We prove an explicit formula for the Poincar\'e polynomials of parabolic character varieties of Riemann surfaces with semisimple local monodromies, which was conjectured by Hausel, Letellier and Rodriguez-Villegas. Using an approach of…
An extension of the Poincar\'e group with half-integer spin generators is explicitly constructed. We start discussing the case of three spacetime dimensions, and as an application, it is shown that hypergravity can be formulated so as to…
A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th…
We associate a polynomial to any diagram of unit cells in the first quadrant of the plane using Kohnert's algorithm for moving cells down. In this way, for every weak composition one can choose a cell diagram with corresponding row-counts,…
$N=2$ coset models of the type $SU(m+1)/SU(m)\times U(1)$ with nondiagonal modular invariants for both $SU(m+1)$ and $SU(m)$ are considered. Poincar\'e polynomials of the corresponding chiral rings of these algebras are constructed. They…
This work is concerned with different aspects of spectrahedra and their projections, sets that are important in semidefinite optimization. We prove results on the limitations of so called Lasserre and theta body relaxation methods for…
Starting from the data of an arbor, which is a rooted tree with vertices decorated by disjoint sets, we introduce a lattice polytope and a partial order on its lattice points. We give recursive algorithms for various classical invariants of…
Poincar\'e series of $p$-adic, definable equivalence relations have been studied in various cases since Igusa's and Denef's work related to counting solutions of polynomial equations modulo $p^n$ for prime $p$. General semi-algebraic…
We study the relation between zero loci of Bernstein-Sato ideals and roots of b-functions and obtain a criterion to guarantee that roots of b-functions of a reducible polynomial are determined by the zero locus of the associated…
F. Gehring and W. Ziemer proved that the p-modulus of the family of paths connecting two continua is dual to the p^*-modulus of the corresponding family of separating hypersurfaces. In this paper we show that a similar result holds in…
We consider a certain linear combination $S(\mathbf{s},\mathbf{y};I;\Delta)$ of zeta-functions of root systems, where $\Delta$ is a root system of rank $r$ and $I\subset\{1,2,\ldots,r\}$. Showing two different expressions of…
In this note, we give some generalisations of the classical Poincar\'{e} upper half-plane, which is the most popular model of hyperbolic plane geometry. For this, we replace the circular arcs by elliptical arcs with center on the $x-$axis,…
We construct an extension of the Poincare group which involves a mixture of internal and space-time supersymmetries. The resulting group is an extension of the superPoincare group with infinitely many generators which carry internal and…
We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincar\'e polynomial. We prove a Terao-type factorization statement on the splitting of…
We study oplax colimits of stable categories, of hermitian categories and of Poincar\'e categories in nice cases. This allows us to produce a categorical model of the assembly map of a bordism-invariant functor of Poincar\'e categories…
We associate a quotient of superspace to any hyperplane arrangement by considering the differential closure of an ideal generated by powers of certain homogeneous linear forms. This quotient is a superspace analogue of the external…
By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann zeta function at positive odd-integer arguments. The explicit expressions enable us to obtain criteria for the dimension of the vector space…
A classical result by Kreweras (1965) allows one to compute the number of plane partitions of a given skew shape and bounded parts as certain determinants. We prove that these determinants expand as polynomials with nonnegative…
We extend previous results about Putinar's Positivstellensatz for cylinders of type $S \times {\mathbb R}$ to sets of type $S \times {\mathbb R}^r$ in some special cases taking into account $r$ and the degree of the polynomial with respect…
In an earlier paper we showed that the radial expansion of a hyperbolic convex set in the Poincar\'e disk about any point inside it results in a hyperbolic convex set. In this work, we generalize this result by showing that the asymmetric…