Results 41 to 50 of about 4,436 (299)
Generating binomial coefficients in a row of Pascal's triangle from extensions of powers of eleven
Heliyon, 2022 Sir Isaac Newton noticed that the values of the first five rows of Pascal's triangle are each formed by a power of 11, and claimed that subsequent rows can also be generated by a power of 11.
Md. Shariful Islam +3 more
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Composite Fermions and Integer Partitions
Journal of Combinatorial Theory, Series A, 2001 The authors prove the unimodality of integer partitions with at most \(a\) parts, all parts less than or equal to \(b\), that are required to contain either repeated or consecutive parts. The proof uses the KOH theorem [\textit{D. Zeilberger}, Am. Math. Mon. 96, No. 7, 590-602 (1989; Zbl 0726.05005)].
Benjamin, Arthur T. +3 more
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Nonlocal Conduction in a Metawire
Advanced Materials, Volume 37, Issue 13, April 2, 2025.A 1D metawire composed of twisted copper wires is designed and realized. This metamaterial exhibits pronounced effects of nonlocal electric conduction according to Ohm's law. The current at one location not only depends on the electric field at that location but also on other locations.
Julio Andrés Iglesias Martínez +3 more
wiley +1 more source
Asymptotic formulas for integer partitions within the approach of microcanonical ensemble
Condensed Matter Physics, 2012 The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary (one-dimensional) partitions,
D. Prokhorov, A. Rovenchak
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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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Integer Partitions with Fixed Subsums [PDF]
The Electronic Journal of Combinatorics, 2005 Given two positive integers $m\le n$, we consider the set of partitions $\lambda=(\lambda_1,\dots,\lambda_\ell,0,\dots)$, $\lambda_1\ge\lambda_2\ge\dots$, of $n$ such that the sum of its parts over a fixed increasing subsequence $(a_j)$ is $m$: $\lambda_{a_1}+\lambda_{a_2}+\dots=m$. We show that the number of such partitions does not depend on $n$ if $
openaire +3 more sources
Opportunities of Semiconducting Oxide Nanostructures as Advanced Luminescent Materials in Photonics
Advanced Materials, EarlyView.The review discusses the challenges of wide and ultrawide bandgap semiconducting oxides as a suitable material platform for photonics. They offer great versatility in terms of tuning microstructure, native defects, doping, anisotropy, and micro‐ and nano‐structuring. The review focuses on their light emission, light‐confinement in optical cavities, and
Ana Cremades +7 more
wiley +1 more source
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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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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Graphene‐Based Wearable Textile Triboelectric Nanogenerators and Biomechanical Sensors
Advanced Materials Technologies, EarlyView.This study presents a wearable textile‐based triboelectric nanogenerator (T‐TENG) using sprayed graphene enhanced with a PVA adhesion layer. The graphene‐based electrode demonstrates high electrical conductivity and robustness to multiple bends. The fabricated T‐TENG provides stable and efficient output, with strong responsiveness to biomotion.
Hongyang Dang +4 more
wiley +1 more source