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A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.

cyclic covering --- monodromy group --- Kongruenzgruppe --- zyklische Überlagerung --- Translationsüberlagerung --- translation coveringVeechgruppe --- congruence subgroup --- Monodromiegruppe --- Veech group

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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

generalized Laguerre --- central complete Bell numbers --- rational polynomials --- Changhee polynomials of type two --- Euler polynomials --- generalized Laguerre polynomials --- Hermite --- conjecture --- Legendre --- the degenerate gamma function --- trivariate Lucas polynomials --- perfectly matched layer --- third-order character --- Euler numbers --- two variable q-Berstein operator --- entropy production --- hypergeometric function --- q-Bernoulli numbers --- q-Bernoulli polynomials --- symmetry group --- Bernoulli polynomials --- Fibonacci polynomials --- central incomplete Bell polynomials --- Chebyshev polynomials --- convolution sums --- Lucas polynomials --- Jacobi --- the modified degenerate Laplace transform --- q-Volkenborn integral on ?p --- and fourth kinds --- two variable q-Berstein polynomial --- the modified degenerate gamma function --- two variable q-Bernstein operators --- reduction method --- identity --- elementary and combinatorial methods --- generalized Bernoulli polynomials and numbers attached to a Dirichlet character ? --- explicit relations --- recursive sequence --- Fubini polynomials --- p-adic integral on ?p --- generating functions --- q-Euler number --- acoustic wave equation --- congruence --- trivariate Fibonacci polynomials --- stochastic thermodynamics --- fermionic p-adic integrals --- Laguerre polynomials --- fluctuation theorem --- Bernoulli numbers and polynomials --- w-torsion Fubini polynomials --- non-equilibrium free energy --- hypergeometric functions 1F1 and 2F1 --- recursive formula --- Chebyshev polynomials of the first --- second --- central complete Bell polynomials --- Apostol-type Frobenius–Euler polynomials --- sums of finite products --- q-Euler polynomial --- symmetric identities --- stability --- fermionic p-adic q-integral on ?p --- Gegenbauer polynomials --- continued fraction --- thermodynamics of information --- well-posedness --- fermionic p-adic integral on ?p --- catalan numbers --- classical Gauss sums --- three-variable Hermite polynomials --- q-Changhee polynomials --- Catalan numbers --- two variable q-Bernstein polynomials --- q-Euler polynomials --- analytic method --- representation --- mutual information --- Fibonacci --- Legendre polynomials --- Gegenbauer --- generalized Bernoulli polynomials and numbers of arbitrary complex order --- Lucas --- elementary method --- new sequence --- third --- the degenerate Laplace transform --- computational formula --- operational connection --- sums of finite products of Chebyshev polynomials of the third and fourth kinds --- Changhee polynomials --- linear form in logarithms