Related papers: Dinv, Area, and Bounce for $\vec{k}$-Dyck paths
We analyze infinite-dimensional Hamiltonian systems corresponding to partial differential equations on one-dimensional spatial domains formulated with formally skew-adjoint Hamiltonian operators and nonlinear Hamiltonian density. In various…
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically…
We present a combinatorial model of configuration spaces and polytopes associated to the quotients of $\mathbb{C} A_n$, the path algebra of the linearly oriented $A_n$ quiver, i.e. the algebra of upper triangular matrices. These quotient…
The aim of this work is to extend to a general $S_m\times S_n$-module context the Grossman-Bizley paradigm that allows the enumeration of Dyck paths in a $m\times n$-rectangle. We obtain an explicit formula for the the "bi-Frobenius"…
In the inclined layer convection system, thermal convection in a Rayleigh--B\'enard cell tilted against gravity, the flow is subject to competing buoyancy and shear forces. For varying inclination angle ($\gamma$) and Rayleigh number…
A geometric p-rough path can be seen to be a genuine path of finite p-variation with values in a Lie group equipped with a natural distance. The group and its distance lift (R^{d},+,0) and its Euclidean distance. This approach allows us to…
We revisit certain path-lifting and path-continuation properties of abstract maps as described in the work of F. Browder and R. Rheindboldt in 1950-1960s, and apply their elegant theory to exponential maps. We obtain thereby a number of…
In a prior paper the authors obtained a four-dimensional discrete integrable dynamical system by the traveling wave reduction from the lattice super-KdV equation in a case of finitely generated Grassmann algebra. The system is a coupling of…
Motivated by the theory of holographic quantum error correction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, together with the kink transform conjecture on the bulk AdS description of boundary cocycle flow, we…
We study a statistic $\mathsf{traj}$ on the ordered pairs $(P,Q)$ of Dyck paths of size $n$, which counts the number of billiard trajectories in the grid polygon enclosed by $P$ and $-Q$, where $-Q$ is the path obtained by reflecting $Q$…
In this paper we deduce the sketch of proof of the Duistermaat-Heckman formula and investigate how the known Duistermaat-Heckman result could be specialized to the symplectic structure on the orbit space. The theorems of localization in…
In this note we discuss dual pairs in Dirac geometry. We show that this notion appears naturally when studying the problem of pushing forward a Dirac structure along a surjective submersion, and we prove a Dirac-theoretic version of…
This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle $\gamma$ and the Rayleigh number $R$.…
The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative…
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the…
In a recent preprint, Matherne, Morales and Selover conjectured that two different representations of unit interval posets are related by the famous zeta map in $q,t$-Catalan combinatorics. This conjecture was proved recently by G\'elinas,…
It is shown that generalized Rota-Baxter operators introduced in [W.A. Martinez, E.G. Reyes & M. Ronco, Int. J. Geom. Meth. Mod. Phys. 18 (2021) 2150176] are a special case of Rota-Baxter systems [T. Brzezi\'nski, J. Algebra 460 (2016),…
The Pelikan random trajectories $x_t \in [0,1[$ are generated by choosing the chaotic doubling map $x_{t+1}=2 x_t [mod 1]$ with probability $p$ and the non-chaotic half-contracting map $x_{t+1}=\frac{x_t}{2}$ with probability $(1-p)$. We…
We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in…
For any orientable compact surface with boundary, we compute the regularized determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values of dynamical zeta functions by using natural uniformizations, one due to…