Related papers: Birational Rowmotion and the Octahedron Recurrence
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a…
We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules. Each globule is a sphere with time-dependent random radius and…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…
We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups…
We review the connections between the octahedral recurrence, $\lambda$-determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the $\lambda$-determinant (and generalizations thereof) of an…
We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal…
Given two regular graphs with consistent rotation maps, we produce a constructive method for a consistent rotation map on their Cartesian product. This method will be given as a simple set of rules of addition and table look ups. We assume…
We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
A Boolean function in $n$ variables is rotation symmetric (RS) if it is invariant under powers of $\rho(x_1, \ldots, x_n) = (x_2, \ldots, x_n, x_1)$. An RS function is called monomial rotation symmetric (MRS) if it is generated by applying…
In this study, we investigate Horadam sequence as generalization of linear recurrence equations of order two. By the aid of this sequence we obtain a new generalization for sequences of dual quaternions and dual octonions. Moreover, we…
We consider two types of trajectories found in a wide range of mechanical systems, viz. box orbits and loop orbits. We elucidate the dynamics of these orbits in the simple context of a perturbed harmonic oscillator in two dimensions. We…
We present a generalization of multiple orthogonal polynomials of type I and type II, which we call multiple orthogonal polynomials of mixed type. Some basic properties are formulated, and a Riemann-Hilbert problem for the multiple…
In a recent paper, Ayyer and Behrend present for a wide class of partitions factorizations of Schur polynomials with an even number of variables where half of the variables are the reciprocals of the others into symplectic and/or orthogonal…
We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by…
Using the lattice paths in $\mathbb{N}\times\mathbb{N}$, we derive a general formula for sequences $\big(T(n,k)\big)$ satisfying the recurrence relation of the form: \begin{equation*} T((n,k)=a_{n,k}T(n-1,k)+b_{n,k}T(n-1,k-1).…
The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect…
For three-body problem, R.Montgomery [3] proved a reconstruction formula which calculates the overall rotation relating two similar triangle configurations if the initial triangular configuration is similar to the configuration formed at…
For an infinite word $x$, Bugeaud and Kim introduced a quantity $\mathrm{rep}(x)$ called the exponent of repetition of $x$. We prove that $\mathrm{rep}(x) = \mathrm{rep}(y)$ holds for a Sturmian word $x$ and every suffix $y$ of $x$. Let $c$…