Results 71 to 80 of about 56,637 (162)
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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Catalan-like numbers and succession rules
, 2005 The ECO method and the theory of Catalan-like numbers introduced by Aigner seems two completely unrelated combinatorial settings. In this work we try to establish a bridge between them, aiming at starting a (hopefully) fruitful study on their ...
Ferrari, Luca, Pinzani, Renzo
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Summation Formulas for Certain Combinatorial Sequences
MathematicsIn this work, we establish some characteristics for a sequence, Aα(n,k), including recurrence relations, generating function and inversion formula, etc.
Yulei Chen, Dongwei Guo
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Set-Valued Tableaux & Generalized Catalan Numbers
, 2017 Standard set-valued Young tableaux are a generalization of standard Young tableaux in which cells may contain more than one integer, with the added conditions that every integer at position $(i,j)$ must be smaller than every integer at positions $(i,j+1)$
Drube, Paul
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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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Communications of the American Mathematical SocietyGiven a (bounded affine) permutation f f , we study the positroid Catalan number C f C_f defined to be the torus-equivariant Euler characteristic of the associated open positroid variety. We introduce a class of repetition-free permutations and show that the corresponding positroid Catalan numbers ...
Galashin, Pavel, Lam, Thomas
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Catalan-like Numbers and Determinants
Journal of Combinatorial Theory, Series A, 1999 The Catalan numbers play a central role in enumerations. They can be defined by recursion but also via so-called Hankel matrices. The Motzkin numbers are defined by a very similar recursion, and Aigner also found a description using Hankel matrices. Both types of numbers are involved in several classical formulae with binomial coefficients (and with ...
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Tableau Cycling and Catalan Numbers
, 2007 We develop two combinatorial proofs of the fact that certain Young tableaux are counted by the Catalan numbers. The setting is a larger class of tableaux where labels increase along rows without attention to whether labels increase down columns. We define a new operation called tableau cycling. It is used to duplicate the reflection argument attributed
Buontempo, Jenny, Hopkins, Brian
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Catalan Numbers for the Classroom?
Elemente der Mathematik, 1997 The author describes the experiences with 13-14 years old pupils in a project on Catalan numbers. She asserts that solving simple combinatorial problems plays an important role in developing thought processes, and should be practised throughout secondary school.
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