Results 41 to 50 of about 111,861 (267)
The Catalan-Qi number of the second kind and a related integral [PDF]
, 2021 Enno Diekema
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, 2020 A finitization of the Catalan numbers $ C_n $ can be defined as Euler characteristics of an algebraic structure. We conjecture the existence of a $ q $-deformed version of such structure, and provide evidence for the first two non-trivial cases. This $ q $-deformed version will likely categorify series arise from identities of the Roger-Ramanujan type.
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Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube
, 2019 We study a two-parameter generalization of the Catalan numbers: $C_{d,p}(n)$ is the number of ways to subdivide the $d$-dimensional hypercube into $n$ rectangular blocks using orthogonal partitions of fixed arity $p$. Bremner \& Dotsenko introduced $C_{d,
Au, Yu Hin +2 more
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Journal of Mathematical Analysis and Applications, 1985 Motivated by author's earlier development of binomial functions [ibid. 70, 460-473 (1979; Zbl 0416.05007); ibid. 83, 110-125 (1981; Zbl 0477.05004)] the notion of Catalan binomial functions, Catalan matrices and that of Sheffer functions is introduced as a generalization of the same named sequences.
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Stochastic Process Leading to Catalan Number Recurrence [PDF]
, 2023 Mariusz Białecki
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Autism Research, EarlyView.ABSTRACT Bilingualism has been associated with enhanced metalinguistic awareness (MA), the ability to reflect upon language. However, findings remain mixed, and little is known about how proficiency in the most proficient (L1) and second‐best language (L2) contribute to MA, especially in children with autism spectrum disorder (ASD), who often present ...
Pauline Wolfer +2 more
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British Educational Research Journal, EarlyView.Abstract School segregation is an international problem undermining the performance and equity of education systems. Australia's secondary schooling system offers international insights into the causes of segregation owing to it being one of the most segregated in the Organisation for Economic Co‐operation and Development, its long history of school ...
Michael G. Sciffer +2 more
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Continued fractions and Catalan problems
, 2000 We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a
Jani, Mahendra, Rieper, Robert G.
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British Educational Research Journal, EarlyView.Abstract This article examines the emotional experiences and processes of stigmatisation encountered by families benefiting from the Shock Plan Against Segregation and for Inclusion, Equal Opportunities and Educational Success (SP), implemented in Barcelona.
Andrea Jover +3 more
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Journal of Combinatorial Theory, Series A, 1994 This paper gives another proof for the well-known fact, that the number of the well-formed orderings of \(n\) open and \(n\) closed parentheses is \({2n\choose n}/(n+1)\). The presented method works partitioning all the possible \({2n\choose n}\) orderings into classes of size \((n+1)\) such that every and each class contains exactly one well-formed ...
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