Results 131 to 140 of about 9,807,843 (352)
Arithmetic of weighted Catalan numbers [PDF]
arXiv, 2019 In this paper, we study arithmetic properties of weighted Catalan numbers. Previously, Postnikov and Sagan found conditions under which the $2$-adic valuations of the weighted Catalan numbers are equal to the $2$-adic valutations of the Catalan numbers. We obtain the same result under weaker conditions by considering a map from a class of functions to $
arxiv
Sequences from Fibonacci to Catalan: A combinatorial interpretation via Dyck paths
RAIRO - Theoretical Informatics and ApplicationsWe use Dyck paths having some restrictions in order to give a combinatorial interpretation for some famous number sequences. Starting from the Fibonacci numbers we show how the k-generalized Fibonacci numbers, the powers of 2, the Pell numbers, the k ...
E. Barcucci, A. Bernini, R. Pinzani
semanticscholar +1 more source
Advances in Mechanochemical Methods for One‐Pot Multistep Organic Synthesis
Chemistry – A European Journal, Accepted Article.Mechanochemical synthesis has emerged as a powerful and more sustainable alternative to conventional solution‐based methods, offering advantages such as no or only minimal solvent use, reduced reaction times, and simplified operational conditions.
Michael Schnürch, Nina Biedermann
wiley +1 more source
The Hessenberg matrices and Catalan and its generalized numbers [PDF]
arXiv, 2018 We present determinantal representations of the Catalan numbers, k-Fuss-Catalan numbers, and its generalized number. The entries of the normalized Hessenberg matrices are the binomial coefficients that related with the enumeration of lattice paths.
arxiv
Catalan Numbers for the Classroom?
Elemente der Mathematik, 1997 • Catalan numbers appear in various mathematical disciplines. By showing pupils different interpretations of the Catalan numbers one can make them aware of links between seemingly unrelated phenomena. • The basic study of Catalan numbers is accessible at pre-university level; it requires no knowledge beyond elementary mathematics.
openaire +3 more sources
Directional Macrocycle Transport, Release, and Recapture Enabled by a Rotaxane Transporter
Chemistry – A European Journal, EarlyView.This study represents a bistable rotaxane that enables the directional shuttling, release, and recapture of a dibenzo‐24‐crown‐8 macrocycle upon addition of suitable chemical stimuli. This two‐step molecular transport and release can be followed by NMR and distinct changes in the molecular fluorescence. Based on rational molecular design, the liberated
Sohom Kundu +3 more
wiley +1 more source
Modifying factors of PD‐L1 expression on tumor cells in advanced non‐small‐cell lung cancer
Thoracic Cancer, Volume 13, Issue 23, Page 3362-3373, December 2022., 2022 Programmed death ligand‐1 (PD‐L1) is an essential biomarker guiding treatment in nononcogene addicted advanced lung adenocarcinoma, and many factors may impact its reproducibility and performance. This study demonstrated an increased probability of identifying PD‐L1‐positive samples in poorly differentiated, solid predominant, and EGFR wild‐type tumors.
Alejandro Avilés‐Salas +11 more
wiley +1 more source
Trajectories and functions of Catalan nationalism since the 19th century
Studies on National Movements, 2014 This article attempts to outline, in a brief summary, the outstanding features of the longue dur trajectories of the movements, concepts, alliances and politics of Catalan nationalism and their functions for Catalan and Spanish politics through the last ...
Hans-Jürgen Puhle
doaj +2 more sources
On the (n,k)-th Catalan numbers [PDF]
Commun. Korean Math. Soc. 23(3) (2008) 349-356, 2015 In this paper, we generalize the Catalan number to the $(n,k)$-th Catalan numbers and find a combinatorial description that the $(n,k)$-th Catalan numbers is equal to the number of partitions of $n(k-1)+2$ polygon by $(k+1)$-gon where all vertices of all $(k+1)$-gons lie on the vertices of $n(k-1)+2$ polygon.
arxiv
Core‐Twisted, Cationic Perylene Diimides; Homochiral Dimerization and Chiroptical Anion Sensing
Chemistry – A European Journal, EarlyView.The installation of two 3‐methyl‐1,2,3‐triazolium heterocycles on the aromatic core of a perylene diimide (PDI) generates a twisted and cationic organic dye. As potent hydrogen bond donors, these groups enable the PDI to self‐assemble into discrete and robust homochiral dimers in solution.
Denis Hartmann +3 more
wiley +1 more source