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Duality triads of higher rank: Further properties and some examples
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In this article, it was shown that duality triads of higher rank are closely related to orthogonal matrix polynomials on the real line, and that the generalized Stirling numbers of rank r give rise to a duality triplet of rank n.Abstract:
It is shown that duality triads of higher rank are closely related to orthogonal matrix polynomials on the real line. Furthermore, some examples of duality triads of higher rank are discussed. In particular, it is shown that the generalized Stirling numbers of rank r give rise to a duality triad of rank r.read more
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Motzkin numbers of higher rank: Generating function and explicit expression
TL;DR: In this paper, the generating function for the colored Motzkin numbers of higher rank was discussed, and explicit expressions for the higher rank case in the first few instances were given.
On the recursion relation of Motzkin numbers of higher rank
TL;DR: In this article, it is proposed that finding the recursion relation and generating function for the colored Motzkin numbers of higher rank is an interesting problem, and it is shown that the problem is NP-hard.
Journal ArticleDOI
The general boson normal ordering problem
TL;DR: In this paper, a generalization of the Bell and Stirling numbers, called generalized combinatorial numbers (GPNs), is proposed for the normal ordering problem of F[(a*)^r a^s], with r,s positive integers.
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Motzkin numbers of higher rank: Generating function and explicit expression
TL;DR: In this article, the generating function and an explicit expression for the colored Motzkin numbers of higher rank were derived for the special case of rank one, and the corresponding results for the conventional colored numbers for which in addition a recursion relation was given.
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Orthogonal Polynomials
TL;DR: In this paper, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed and orthogonality on the unit circle is not discussed.
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The theory of partitions
TL;DR: The elementary theory of partitions and partitions in combinatorics can be found in this article, where the Hardy-Ramanujan-Rademacher expansion of p(n) is considered.