Related papers: Birational rowmotion on a rectangle over a noncomm…
A derangement is a permutation with no fixed point, and a nonderangement is a permutation with at least one fixed point. There is a one-term recurrence for the number of derangements of $n$ elements, and we describe a bijective proof of…
We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory. Firstly…
An area-preserving homeomorphism isotopic to the identity is said to have rational rotation direction if its rotation vector is a real multiple of a rational class. We give a short proof that any area-preserving homeomorphism of a compact…
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find numerical approximations of such objects. Our approach…
This paper is devoted to periodic travelling waves solving Lie-Poisson equations based on the Virasoro group. We show that the reconstruction of any such solution can be carried out exactly, regardless of the underlying Hamiltonian (which…
Nicaise--Ottem introduced the notion of (stably) rational polytopes and studied this using a combinatorial description of the motivic volume. In this framework, we ask whether being non-stably rational is preserved under inclusions. We…
We construct an upgrade of the motivic volume by keeping track of dimensions in the Grothendieck ring of varieties. This produces a uniform refinement of the motivic volume and its birational version introduced by Kontsevich and Tschinkel…
Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…
We study cocycles (non-autonomous dynamical systems) satisfying a certain squeezing condition with respect to the quadratic form of a bounded self-adjoint operator acting in a Hilbert space. We prove that (under additional assumptions) the…
Billey-Postnikov (BP) decompositions govern when Schubert varieties $X(w)$ decompose as bundles of smaller Schubert varieties. We further develop the theory of BP decompositions and show that, in finite type, they can be recognized by…
Uneven terrain necessarily transforms periodic walking into a non-periodic motion. As such, traditional stability analysis tools no longer adequately capture the ability of a bipedal robot to locomote in the presence of such disturbances.…
We construct an algebraic commutative ring T- spectrum BO which is stably fibrant and (8,4)- periodic and such that on SmOp/S the cohomology theory (X,U) -> BO^{p,q}(X_{+}/U_{+}) and Schlichting's hermitian K-theory functor (X,U) ->…
A barcode is a finite multiset of intervals on the real line, $B = \{ (b_i, d_i)\}_{i=1}^n$. Barcodes are important objects in topological data analysis, where they serve as summaries of the persistent homology groups of a filtration. The…
For every nontrivial free homotopy class $\alpha$ of loops in every closed connected Riemannian manifold $M$, we prove existence of a noncontractible 1-periodic orbit, for every compactly supported time-dependent Hamiltonian on the open…
Brualdi and Ma found a connection between involutions of length $n$ with $k$ descents and symmetric $k\times k$ matrices with non-negative integer entries summing to $n$ and having no row or column of zeros. From their main theorem they…
From Smyth's classification, modular compactifications of pointed smooth rational curves are indexed by combinatorial data, so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a…
We study restricted chain-order polytopes associated to Young diagrams using combinatorial mutations. These polytopes are obtained by intersecting chain-order polytopes with certain hyperplanes. The family of chain-order polytopes…
Over an arbitrary commutative ring, correspondences among three sets, the set of trace ideals, the set of stable ideals, and the set of birational extensions of the base ring, are studied. The correspondences are well-behaved, if the base…
This paper introduces two matrix analogues for set partitions. A composition matrix on a finite set X is an upper triangular matrix whose entries partition X, and for which there are no rows or columns containing only empty sets. A…
For $S$ a very general polarized K3 surface of degree $8n-6$, we describe in geometrical terms a birational involution of the Hilbert scheme $S^{[n]}$ of $n$ points on the surface, whose existence was established from lattice theoretical…