Related papers: Birational rowmotion on a rectangle over a noncomm…
The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…
We analyze a random lozenge tiling model of a large regular hexagon, whose underlying weight structure is periodic of period $2$ in both the horizontal and vertical directions. This is a determinantal point process whose correlation kernel…
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the…
For an alternate base $\boldsymbol{\beta}=(\beta_0,\ldots,\beta_{p-1})$, we show that if all rational numbers in the unit interval $[0,1)$ have periodic expansions with respect to the $p$ shifts of $\boldsymbol{\beta}$, then the bases…
We study four bijections, which are promotion, evacuation, rowmotion, and rowvacuation, on generalized Dyck paths in rational Catalan combinatorics. We define the maps on generalized Dyck paths, which have their origins in maps on Dyck…
In 2024, Ceballos and Chenevi{\`e}re introduced alt $\nu$-Tamari lattices, parameterized by a lattice path $\nu$ and an increment vector $\delta$, as a common generalization of $\nu$-Tamari and $\nu$-Dyck lattices. We study rowmotion on two…
Commutative totally ordered monoids abound, number systems for example. When the monoid is not assumed commutative, one may be hard pressed to find an example. One suggested by Professor Orr Shalit are the countable ordinals with addition.…
The combinatorial mutation $\mathrm{mut}_w(P,F)$ for a lattice polytope $P$ was introduced in the context of mirror symmetry for Fano manifolds in [1]. It was also proved in [1] that for a lattice polytope $P \subseteq N_\mathbb{R}$…
How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given…
Recently, there has been a lot of work on combinatorial inequalities related to hook-lengths in $t$-regular partitions. In this short note, we give a proof using generating functions for a result proved by Singh and Barman (2026) using…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
We study the dynamics of the piecewise planar rotations $F_{\lambda}(z)=\lambda (z-H(z)), $ with $z\in\C$, $H(z)=1$ if $\mathrm{Im}(z)\ge0,$ $H(z)=-1$ if $\mathrm{Im}(z)<0,$ and $\lambda=\mathrm{e}^{i \alpha} \in\C$, being $\alpha$ a…
In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to…
Bott periodicity plays an important role in topological K-theory. The purpose of this paper is to extend the periodicity theorem in a discrete context, where all classical groups are involved and not just the general linear group. The…
Recently, dispersionless (coherent) motion of (noninteracting) massive Brownian particles, at intermediate time scales, was reported in a sinusoidal potential with a constant tilt. The coherent motion persists for a finite length of time…
Sch\"{u}tzenberger's promotion operator is an extensively-studied bijection that permutes the linear extensions of a finite poset. We introduce a natural extension $\partial$ of this operator that acts on all labelings of a poset. We prove…
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…
We address the general problem of studying linear stability and bifurcations of periodic orbits for Hamiltonian systems of arbitrary degrees of freedom. We study the topology of the GIT sequence introduced by the first author and Urs…
Networks of elastoplastic springs (elastoplastic systems) have been linked to differential equations with polyhedral constraints in the pioneering paper by Moreau (1974). Periodic loading of an elastoplastic system, therefore, corresponds…
Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. Applications include…