Related papers: Non-normal very ample polytopes - constructions an…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this paper we consider invariant formulation of nonlinear (Lagrangian…
There are natural polynomial invariants of polytopes and lattice polytopes coming from enumerative combinatorics and Ehrhart theory, namely the $h$- and $h^*$-polynomials, respectively. In this paper, we study their generalization to…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
If $P$ is a lattice polytope (i.e., $P$ is the convex hull of finitely many integer points in $\mathbb{R}^d$) of dimension $d$, Ehrhart's famous theorem (1962) asserts that the integer-point counting function $|nP \cap \mathbb{Z}^d|$ is a…
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.
A lattice polytope translated by a rational vector is called an almost integral polytope. In this paper we investigate Ehrhart quasi-polynomials of almost integral polytopes. We study the relationship between the shape of the polytopes and…
A formulation is given for the spectral transformation of the generalized eigenvalue problem through the decomposition of the second-order differential operators. This allows us to construct some Laurent biorthogonal polynomial systems with…
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…
We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the…
The Tur\'{a}n problem asks for the largest number of edges ex$(n,H)$ in an $n$-vertex graph not containing a fixed forbidden subgraph $H$, which is one of the most important problems in extremal graph theory. However the order of magnitude…
We compare the deformation theory and the analytic structure of the Seiberg-Witten moduli spaces of a K\"ahler surface to the corresponding components of the Hilbert scheme, and show that they are isomorphic. Next we show how to compute the…
We consider a class of $0$-$1$ polynomial programming termed multiple choice polynomial programming (MCPP) where the constraint requires exact one component per subset of the partition to be $1$ after all the entries are partitioned.…
We give the first exact and stability results for a hypergraph Tur\'{a}n problem with infinitely many extremal constructions that are far from each other in edit-distance. This includes an example of triple systems with Tur\'{a}n density…
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
It is known that the extension complexity of the TSP polytope for the complete graph $K_n$ is exponential in $n$ even if the subtour inequalities are excluded. In this article we study the polytopes formed by removing other subsets…
We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…
Building on the work of Nenciu we provide examples of non-factorizable ribbon Hopf algebras, and introduce a stronger notion of non-factorizability. These algebras are designed to provide invariants of $4$-dimensional $2$-handlebodies up to…
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geometric questions about these models, such as determining the…
This paper continues our researches \cite{DS1, DS2, DS3} by computing some invariants based on Hilbert-Poincar\'{e} series associated to Milnor algebras. Our computations are for some of the classical surfaces and 3-folds with different…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…