Results 11 to 20 of about 582,984 (315)
Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order
MathematicsWe study the formulas for binomial sums of harmonic numbers of higher order ∑k=0nHk(r)nk(1−q)kqn−k=Hn(r)−∑j=1nDr(n,j)qjj. Recently, Mneimneh proved that D1(n,j)=1. In this paper, we find several different expressions of Dr(n,j) for r≥1.
Takao Komatsu, B. Sury
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Polynomial Approach to Explicit Formulae for Generalized Binomial Coefficients [PDF]
, 2015 We extend the polynomial approach to the hook length formula proposed in Károlyi et al. Adv Math 277:252–282 (2015) to several other problems of the same type, including the number of paths formula in the Young graph of strict partitions.
Fedor Petrov
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Polynomial sequences of binomial-type arising in graph theory [PDF]
, 2012 In this paper, we show that the solution to a large class of "tiling" problems is given by a polynomial sequence of binomial type. More specifically, we show that the number of ways to place a fixed set of polyominos on an $n\times n$ toroidal chessboard
Schneider, Jon
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From the binomial reshuffling model to Poisson distribution of money [PDF]
Networks and Heterogeneous Media, 2022 We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth $ X_i $ and $ X_j $ are redistributed by flipping a sequence of fair coins leading to a binomial ...
Fei Cao, Nicholas F. Marshall
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New Class of Quantum Error-Correcting Codes for a Bosonic Mode
Physical Review X, 2016 We construct a new class of quantum error-correcting codes for a bosonic mode, which are advantageous for applications in quantum memories, communication, and scalable computation.
Marios H. Michael +6 more
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The Binomial-Stirling-Eulerian Polynomials [PDF]
European Journal of Combinatorics, 2023 We introduce the binomial-Stirling-Eulerian polynomials, denoted $\tilde{A}_n(x,y|α)$, which encompass binomial coefficients, Eulerian numbers and two Stirling statistics: the left-to-right minima and the right-to-left minima. When $α=1$, these polynomials reduce to the binomial-Eulerian polynomials $\tilde{A}_n(x,y)$, originally named by Shareshian ...
Kathy Q. Ji, Lin, Zhicong
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Schur type functions associated with polynomial sequences of binomial type [PDF]
, 2007 .We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions.
Minoru Itoh
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Polynomial Sequences of Binomial-Type Arising in Graph Theory [PDF]
Electronic Journal of Combinatorics, 2014 In this paper, we show that the solution to a large class of "tiling'' problems is given by a polynomial sequence of binomial type. More specifically, we show that the number of ways to place a fixed set of polyominos on an $n\times n$ toroidal ...
Jonathan Schneider
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On binomial operator representations of certain polynomial [PDF]
Proyecciones (Antofagasta), 2011 Based on the technique used by M.A.Khanand A. K. Shukla [4] here finite series representations of binomial partial differential operators have been used to establish operator representations of various polynomials not considered in the earlier mentioned ...
M. Khan, K. Nisar
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Binomial Fibonacci sums from Chebyshev polynomials [PDF]
, 2023 25 ...
Kunle Adegoke +2 more
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