Results 71 to 80 of about 1,690,008 (302)
Bijections between noncrossing and nonnesting partitions for classical reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We present $\textit{type preserving}$ bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types $B$, $C$ and $D$ are new in
Alex Fink, Benjamin Iriarte Giraldo
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Journal of Combinatorial Theory, Series A, 1985 Let \(C_ n\) be the set of Catalan words: binary words with n zeros and n ones such that each initial segment has at least as many zeros and ones. For \(w\in C_ n\), let d(w) be the number of descents, a(w) be the sum over all descents of the number of zeros to the left, b(w) be the sum over all descents of the number of ones to the left.
Fürlinger, J, Hofbauer, J
openaire +1 more source
Advanced Science, EarlyView.ABSTRACT The combination of metasurfaces with chalcogenide phase‐change materials is a highly promising route toward the development of multifunctional and reconfigurable nanophotonic devices. However, their transition into real‐world devices is hindered by several technological challenges. This includes, amongst others, the lack of large area photonic
Carlota de Ruiz de Galarreta +8 more
wiley +1 more source
Growing and Destroying Catalan-Stanley Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers.
Benjamin Hackl, Helmut Prodinger
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A combinatorial identity with application to Catalan numbers
, 2005 By a very simple argument, we prove that if $l,m,n$ are nonnegative integers then $$\sum_{k=0}^l(-1)^{m-k}\binom{l}{k}\binom{m-k}{n}\binom{2k}{k-2l+m} =\sum_{k=0}^l\binom{l}{k}\binom{2k}{n}\binom{n-l}{m+n-3k-l}.
Pan, Hao, Sun, Zhi-Wei
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The inverse of a triangular matrix and several identities of the Catalan numbers
Applicable Analysis and Discrete Mathematics, 2019 In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating
Feng Qi (祁锋) +2 more
semanticscholar +1 more source
Stable Diffusion Models Reveal a Persisting Human–AI Gap in Visual Creativity
Advanced Science, EarlyView.This study examines visual creativity in humans and generative AI using the TCIA framework. Human artists outperform AI overall, yet structured human guidance substantially improves AI outputs and evaluations. Findings reveal that alignment with human creativity depends critically on contextual framing, highlighting both the promise and current ...
Silvia Rondini +8 more
wiley +1 more source
Product of Ginibre matrices: Fuss-Catalan and Raney distributions
, 2011 Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distribution P_s(x), such that their moments are equal to the Fuss-Catalan numbers or order s.
Penson, Karol A., Zyczkowski, Karol
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Advanced Science, EarlyView.We investigate whether Montessori and traditional schooling systems shape the developmental trajectory of large‐scale brain dynamics in different ways. We quantify the arrow of time (“non‐reversibility”) in neural activity during resting state and movie‐watching, revealing distinct maturational patterns.
Elvira del Agua +6 more
wiley +1 more source
On generalized bihyperbolic Mersenne numbers [PDF]
Mathematica BohemicaIn this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
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