Results 61 to 70 of about 863,417 (323)
Padovan numbers as sums over partitions into odd parts
Journal of Inequalities and Applications, 2016 Recently it was shown that the Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. In this paper, we introduce a similar representation for the Padovan numbers. As a corollary, we derive
Cristina Ballantine, Mircea Merca
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A generalisation of two partition theorems of Andrews [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur’s celebrated partition identity (1926). Andrews’ two generalisations of Schur’s theorem went on to become two of the most influential results in ...
Jehanne Dousse
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Approximately Sampling Elements with Fixed Rank in Graded Posets
, 2016 Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for counting and ...
Bhakta, Prateek +3 more
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Assessing the Ecological Value: Monetizing Process Innovations in Tailored Forming
Advanced Engineering Materials, EarlyView.This article introduces a method for evaluating the sustainability of innovations, even with limited data. The method is illustrated through an analysis of the “Tailored Forming” technology, which explores the impact of sustainability on economic value added.
Jonas Schneider +4 more
wiley +1 more source
Arc Spaces and Rogers-Ramanujan Identities [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan Identities.
Clemens Bruschek +2 more
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AROUND THE ERDÖS–GALLAI CRITERION
Ural Mathematical Journal, 2023 By an (integer) partition we mean a non-increasing sequence \(\lambda=(\lambda_1, \lambda_2, \dots)\) of non-negative integers that contains a finite number of non-zero components. A partition \(\lambda\) is said to be graphic if there exists a graph \(G\
Vitaly A. Baransky, Tatiana A. Senchonok
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On the Singularity of Random Bernoulli Matrices— Novel Integer Partitions and Lower Bound Expansions [PDF]
, 2011 We prove a lower bound expansion on the probability that a random ±1 matrix is singular, and conjecture that such expansions govern the actual probability of singularity. These expansions are based on naming the most likely, second most likely, and so on,
R. Arratia, S. Desalvo
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2D Borophene: In‐Plane Hyperbolic Polaritons in the Visible Spectral Range
Advanced Functional Materials, EarlyView.Researchers have synthesized the χ3 phase of borophene, a 2D metal, using chemical vapor deposition. Combining theory and deep‐subwavelength spectroscopy, they uncover borophene's unique anisotropic optical behavior in the visible range. This breakthrough paves the way for advanced optoelectronic devices using borophene‐based heterostructures ...
Yaser Abdi +5 more
wiley +1 more source
On Partitions and Arf Semigroups
Open Mathematics, 2019 In this study we examine some combinatorial properties of the Arf semigroup. In previous work, the author and Karakaş, Gümüşbaş defined an Arf partition of a positive integer n. Here, we continue this work and give new results on Arf partitions.
Tutaş Nesrin
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A statistical mechanical approach to restricted integer partition functions
, 2018 The main aim of this paper is twofold: (1) Suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions --- a way of writing an integer as a sum ...
Dai, Wu-Sheng, Zhou, Chi-Chun
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