Results 81 to 90 of about 1,655,826 (313)
Closed form evaluations of some series involving Catalan numbers [PDF]
, 2014 Closed form evaluations of some infinite series comprising sums of exponentiated multiples of Catalan numbers are yielded by a known expansion of the trigonometric function sin(2α), and then re-formulated independently as ...
Larcombe, Peter J.
core
Some combinatorial identities containing central binomial coefficients or Catalan numbers*
Applied Mathematics in Science and Engineering, 2023 In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
doaj +1 more source
Spin‐Split Edge States in Metal‐Supported Graphene Nanoislands Obtained by CVD
Advanced Materials, EarlyView.Combining STM measurements and ab‐initio calculations, we show that zig‐zag edges in graphene nanoislands grown on Ni(111) by CVD retrieve their spin‐polarized edge states after intercalation of a few monolayers of Au. ABSTRACT Spin‐split states localized on zigzag edges have been predicted for different free‐standing graphene nanostructures.
Michele Gastaldo +6 more
wiley +1 more source
On certain series expansions of the sine function: Catalan numbers and convergence [PDF]
, 2014 The appearance of Catalan numbers in certain infinite series expansions of the sine function was first reported well over a decade ago. A combination of computation and analysis is employed as we return to this topic and examine the outstanding issue of ...
Larcombe, Peter J. +2 more
core
Moments on Catalan numbers [PDF]
, 2009 By combining inverse series relations with binomial convolutions and telescoping method, moments of Catalan numbers are evaluated, which resolves a problem recently proposed by Gutiérrez et al. [J.M. Gutiérrez, M.A. Hernández, P.J. Miana, N.
Chen, Xiaojing, Chu, Wenchang
core +1 more source
A Note on Degenerate Catalan-Daehee Numbers and Polynomials [PDF]
, 2022 In this paper, we consider the degenerate forms of the Catalan–Daehee polynomials and numbers by the Volkenborn integrals and obtain diverse explicit expressions and formulas. Moreover, we show the expressions of the degenerate Catalan–Daehee
Ugur Duran +2 more
core +1 more source
Delannoy numbers and Legendre polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We construct an $n$-dimensional polytope whose boundary complex is compressed and whose face numbers for any pulling triangulation are the coefficients of the powers of $(x-1)/2$ in the $n$-th Legendre polynomial.
Gábor Hetyei
doaj +1 more source
COFs on MOFs: Layer‐by‐Layer Synthesis of MOF@COF Nanoparticles with Synergistic Adsorption
Advanced Materials, EarlyView.A layer‐by‐layer strategy enables the growth of crystalline covalent organic framework (COF) shells on metal–organic framework nanoparticles, creating core–shell structures with tunable porosity. Ordered interstitial mesopores are formed during shell growth, which are connected with the COF's intrinsic micropores, thereby enhancing water sorption. This
Ana Guillem‐Navajas +11 more
wiley +1 more source
Combinatorial Interpretations Of Generalizations Of Catalan Numbers And Ballot Numbers [PDF]
, 2018 The super Catalan numbers T(m,n) = (2m)!(2n)!=2m!n!(m+n)! are integers which generalize the Catalan numbers. Since 1874, when Eugene Catalan discovered these numbers, many mathematicians have tried to find their combinatorial interpretation.
Emily Allen (5463164)
core +1 more source
Permutations avoiding an increasing number of length-increasing forbidden subsequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2000 A permutation π is said to be τ -avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ . This paper concerns the characterization and enumeration of permutations which avoid a set F^j of subsequences increasing ...
Elena Barcucci +3 more
doaj +1 more source