Dunkl kernel associated with dihedral groups

Radial Dunkl Processes Associated with Dihedral Systems

We give some interest in radial Dunkl processes associated with dihedral systems. We write down the semi group density and as a by-product the generalized Bessel function and the W -invariant generalized Hermite polynomials. Then, a skew product decomposition, involving only independent Bessel processes, is given and the tail distribution of the first hitting time of boundary of the Weyl chambe...

Polynomials Associated with Dihedral Groups

Abstract. There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The ...

Dihedral Groups

Sumsets in dihedral groups

Let Dn be the dihedral group of order 2n. For all integers r, s such that 1 ≤ r, s ≤ 2n, we give an explicit upper bound for the minimal size μDn (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of Dn of cardinality r and s respectively. It is shown by construction that μDn (r, s) is bounded above by the known value of μG (r, s), where G is any abelian ...

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...