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For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental…
We generalize several classical results about Schur functions to the family of cylindric Schur functions. First, we give a combinatorial proof of a Murnaghan--Nakayama formula for expanding cylindric Schur functions in the power-sum basis.…
For a periodically perforated structure, for which homogenization takes place in the linear theory of elasticity, the components of the effective elasticity tensor depend in general on the geometry of the holes as well as on the local…
We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective flat schemes over Z with a tame action of a finite abelian group. This formula…
The action of the Bernstein operators on Schur functions was given in terms of codes in [CG] and extended to the analog in Schur Q-functions in [HJS]. We define a new combinatorial model of extended codes and show that both of these results…
We describe a new way to construct finite geometric objects. For every k we obtain a symmetric configuration E(k-1) with k points on a line. In particular, we have a constructive existence proof for such configurations. The method is very…
The Kirillov--Schilling--Shimozono (KSS) bijection appearing in theory of the Fermionic formula gives an one to one correspondence between the set of elements of tensor products of the Kirillov--Reshetikhin crystals (called paths) and the…
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…
We introduce a ring of noncommutative shifted symmetric functions based on an integer-indexed sequence of shift parameters. Using generating series and quasideterminants, this multiparameter approach produces deformations of the ring of…
We examine the construction of the spin angular momentum in systems with pseudoclassical Grassmann variables. In constrained systems there are many different algebraic forms for the dynamical variables that will all agree on the constraint…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
Complicated cosmic string loops will fragment until they reach simple, non-intersecting ("stable") configurations. Through extensive numerical study we characterize these attractor loop shapes including their length, velocity, kink, and…
A multistable system generated by a Piecewise Linear (PWL) system based on the jerky equation is presented. The systems behaviour is characterised by means of the Nearest Integer or round(x) function to control the switching events and to…
In this paper, the connections are investigated between two different approaches towards the parametrization of multivariable stable all-pass systems in discrete-time. The first approach involves the tangential Schur algorithm, which…
Hard sphere systems are often used to model simple fluids. The configuration spaces of hard spheres in a three-dimensional torus modulo various symmetry groups are comparatively simple, and could provide valuable information about the…
We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We…
We give lowed bounds on the number of periodic trajectories in strictly convex smooth billiards in $\R^{m+1}$ for $m\ge 3$. For plane billiards (when m=1) such bounds were obtained by G. Birkhoff in the 1920's. Our proof is based on…
Structures with artificial mechanical properties, often called mechanical metamaterials, exhibit divergent yet tunable performance. Various types of mechanical metamaterials have been proposed, which harness light or magnetic interactions,…