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Recent developments in combinatorial aspects of normal ordering
Enumerative Combinatorics and Applications, 2021 In this paper, we report on recent progress concerning combinatorial aspects of normal ordering. After giving a short introduction to the history and motivation of normal ordering, we present some recent developments.
M. Schork
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Poly-falling factorial sequences and poly-rising factorial sequences
Open Mathematics, 2021 In this paper, we introduce generalizations of rising factorials and falling factorials, respectively, and study their relations with the well-known Stirling numbers, Lah numbers, and so on.
Kim Hye Kyung
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Row bounds needed to justifiably express flagged Schur functions with Gessel-Viennot determinants [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Let $\lambda$ be a partition with no more than $n$ parts. Let $\beta$ be a weakly increasing $n$-tuple with entries from $\{ 1, ... , n \}$. The flagged Schur function in the variables $x_1, ...
Robert A. Proctor, Matthew J. Willis
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Associated r-Dowling numbers and some relatives
, 2021 In this paper, we introduce a new generalization of Bell numbers, the s-associated r -Dowling numbers by combining two investigational directions. Here, r distinguished elements have to be in distinct blocks, some elements are coloured according to a ...
Eszter Gyimesi, Gábor Nyul
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Special Matrices, 2023 Denote by σn{\sigma }_{n} the n-th Stirling polynomial in the sense of the well-known book Concrete Mathematics by Graham, Knuth and Patashnik. We show that there exist developments xσn(x)=∑j=0n(2jj!)−1qn−j(j)xjx{\sigma }_{n}\left(x)={\sum }_{j=0}^{n ...
Kovačec Alexander +1 more
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On sums with generalized harmonic, hyperharmonic and special numbers
Miskolc Mathematical Notes, 2020 In this paper, we establish interesting sums including generalized harmonic numbers and special numbers by using generating functions of these numbers and some combinatorial identities.
Ö. Duran, N. Ömür, S. Koparal
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A note on polyexponential and unipoly Bernoulli polynomials of the second kind
Open Mathematics, 2021 In this paper, the authors study the poly-Bernoulli numbers of the second kind, which are defined by using polyexponential functions introduced by Kims. Also by using unipoly function, we study the unipoly Bernoulli numbers of the second kind, which are ...
Ma Minyoung, Lim Dongkyu
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Compositions of positive integers with 2s and 3s
Demonstratio Mathematica, 2023 In this article, we consider compositions of positive integers with 2s and 3s. We see that these compositions lead us to results that involve Padovan numbers, and we give some tiling models of these compositions.
Dişkaya Orhan, Menken Hamza
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Negative moments of orthogonal polynomials
Forum of Mathematics, Sigma, 2023 If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence.
Jihyeug Jang +4 more
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Representations by degenerate Daehee polynomials
Open Mathematics, 2022 In this paper, we consider the problem of representing any polynomial in terms of the degenerate Daehee polynomials and more generally of the higher-order degenerate Daehee polynomials.
Kim Taekyun +3 more
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