Related papers: Self-commuting lattice polynomial functions
An asymptotic formula is presented for the number of planar lattice convex polygonal lines joining the origin to a distant point of the diagonal. The formula involves the non-trivial zeros of the zeta function and leads to a necessary and…
We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.
A simple extension of the Lattice Boltzmann equation is proposed, which permits to handle reactive flow dynamics in the limit of fast chemistry at virtually no extra-cost with respect to the purely hydrodynamic scheme.
We characterize the finite intervals of the Muchnik lattice by proving that they are a certain proper subclass of the finite distributive lattices.
We discuss how lattice calculations can be a useful tool for the study of structure functions. Particular emphasis is given to the perturbative renormalization of the operators.
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact…
We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-commutation relation. This implies that quadratic harnesses are…
We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack…
Let $f, g, h\in \mathbb{C}\left[x\right]$ be non-constant complex polynomials satisfying $f(x)=g(h(x))$ and let $f$ be lacunary in the sense that it has at most $l$ non-constant terms. Zannier proved that there exists a function $B_1(l)$ on…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
In addition to self-propulsion by phoretic mechanisms that arises from an asymmetric distribution of reactive species around a catalytic motor, spherical particles with a uniform distribution of catalytic activity may also propel themselves…
Consider a lattice in a real finite dimensional vector space. Here, we are interested in the lattice polytopes, that is the convex hulls of finite subsets of the lattice. Consider the group $G$ of the affine real transformations which map…
We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices.…
Simple necessary and sufficient conditions for a $n$-tuple of noncommutative polynomials to be a cyclic gradient are given and similarly for a noncommutative polynomial to have a vanishing cyclic gradient. Connections with free probability…
We consider a simple model of the dynamics of a single electron in a crystal lattice. Although this is a standard problem in condensed matter physics, alternative ways of evaluating a partition function for such a system lead to equalities,…
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.