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In this paper, we propose and analyze a third-order dynamical system for solving a generalized inverse mixed variational inequality problem in a Hilbert space H. We establish the existence and uniqueness of the trajectories generated by the…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
We study the spontaneous motion, binary collisions, and collective dynamics of "polar disks", i.e. purpose-built particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their…
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an…
We introduce a new partial order on the set of all antichains of a fixed size in any poset. When applied to minuscule posets, these partial orders give rise to distributive lattices that appear in the branching rules for minuscule…
We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove that these posets are graded by the length function and that…
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…
We discover unexpected connections between packing configurations and rare fluctuations in dense systems of active particles subject to pulsation of size. Using large deviation theory, we examine biased ensembles which select atypical…
We establish formulas for the number of all downsets (or equivalently, of all antichains) of a finite poset P. Then, using these numbers, we determine recursively and explicitly the number of all posets having a fixed set of minimal points…
We study experimentally the nonequilibrium phase behaviour of a horizontal monolayer of macroscopic rods. The motion of the rods in two dimensions is driven by vibrations in the vertical direction. Aside from the control variables of…
We introduce a new statistic on the hyperoctahedral groups (Coxeter groups of type B), and give a conjectural formula for its signed distributions over arbitrary descent classes. The statistic is analogous to the classical Coxeter length…
We characterize the finite distributive lattices which admit a complete valuation, that is bijective over a set of consecutive natural numbers, with the additional conditions of completeness (Definition 2.3). We prove that such lattices are…
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of two dimensional zonotopes, using dynamical systems and order theory. We show that the sets of partitions ordered with a simple…
We prove that a monomial ideal $I$ generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal generators induced by every ordering of variables. We also…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
A planar order is a special linear extension of the edge poset (partially ordered set) of a processive plane graph. The definition of a planar order makes sense for any finite poset and is equivalent to the one of a conjugate order. Here it…
We study matching problems in which agents form one side of a bipartite graph and have preferences over objects on the other side. A central solution concept in this setting is popularity: a matching is popular if it is a (weak) Condorcet…
We study the behavior of moving Bose-Bose mixtures in a weak disordered potential in the realm of the Bogoliubov-Huang-Meng theory. Corrections due to the quantum fluctuations, disorder effects and the relative motion of two fluids to the…
We experimentally study a monolayer of vibrated disks with a built-in polar asymmetry which enables them to move quasi-balistically on a large persistence length. Alignment occurs during collisions as a result of self-propulsion and hard…
We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree expectations (CDE) property. Actually our theorem applies…