Results 31 to 40 of about 246,865 (191)

Brauer Configuration Algebras Induced by Integer Partitions and Their Applications in the Theory of Branched Coverings

Mathematics
Brauer configuration algebras are path algebras induced by appropriated multiset systems. Since their structures underlie combinatorial data, the general description of some of their algebraic invariants (e.g., their dimensions or the dimensions of their
Agustín Moreno Cañadas, José Gregorio Rodríguez-Nieto, Olga Patricia Salazar Díaz   +2 more
doaj   +1 more source

The lattice of integer partitions

Discrete Mathematics, 1973
AbstractIn this paper we study the lattice Ln of partitions of an integer n ordered by dominance. We show Ln to be isomorphic to an infimum subsemilattice under the component ordering of certain concave nondecreasing (n+1)-tuples. For Ln, we give the covering relation, maximal covering number, minimal chains, infimum and supremum irreducibles, a chain ...
openaire   +2 more sources

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   +4 more sources

FastNano Liquid: An Automated Platform for Small‐Angle X‐ray Scattering‐Based Materials Discovery

Advanced Engineering Materials, EarlyView.
We present FastNano Liquid, an automated small‐ and wide‐angle X‐ray scattering platform for the combined synthesis and characterization of (nano)materials. The platform is coupled to varied reactor workflows for both in situ studies of reaction kinetics and ex situ screening of synthesis conditions to support machine learning‐guided exploration ...
Pierre‐Baptiste Flandrin, Émeline Cournède, Jens Krarup, Michael Lesa, Foyzul Hasan, Amandine Séné, Arnaud Lahouati, David Benhaiem, Jérémie‐Luc Sanchez, Simon Delacroix, Thierry Gacoin, Fabienne Testard, Damien Faivre, David Carriere, Corinne Chevallard, Olivier Taché, Mark A. Levenstein   +16 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
doaj   +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
doaj   +1 more source

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, Md. Robiul Islam, Md. Shorif Hossan, Md. Hasan Kibria   +3 more
doaj   +1 more source

From Photoalignment to Structured Light: Liquid Crystal Platforms for Beam Shaping and Complex Wavefronts

Advanced Functional Materials, EarlyView.
Photoaligned and photopatterned liquid crystal platforms provide programmable control of optical phase, polarization, and spin‐orbit interactions, enabling compact generation of structured light and complex wavefronts. This review highlights how tailored molecular orientations transform simple beams into designed optical fields, opening versatile ...
Le Zhou, Tingjun Zhong, Sijie Liu, Pouya Nosratkhah, Ke Xu, Yuzhen Zhao, Kristiaan Neyts   +6 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, Hussein Mourtada, Jan Schepers   +2 more
doaj   +1 more source

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
doaj   +1 more source