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We generalize this statistic and derive an explicit formula for the number of Dyck paths of length 2 n according to the statistic “number of uu · · · udu ’s” (“number of udud ·
properties of orbit functions described in this paper are implications of properties either of orbits of the group W (for description of reflection groups see, for example, [ 17 ] and
Gegenbauer polynomials, as reproducing kernels for the spaces of spherical harmonics of a given degree, or more generally, as providing an explicit construction of symmetry
For a description of transitive and indecomposable systems of two subspaces of a Hilbert space, as well as for transitive and indecomposable triples of a finite dimensional
As it was demonstrated recently, the approach first proposed in [13, 14] based on some set of q - deformed oscillators along with the related model of ideal gas of q -bosons is
[16] Atoyan A., Patera J., Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization, J. [21] Humphreys J., Introduction to
Rather it classifies integrable quantum field theoretic models and in addition provides their explicit exact solutions in term of all Wightman functions.. We achieve contact with
We study multivariable Christoffel–Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation func- tions for
