Success Run Waiting Times and Fuss-Catalan Numbers
نویسندگان
چکیده
منابع مشابه
Multivariate Fuss-Catalan numbers
are integers that appear in many combinatorial problems. These numbers first arose in the work of Catalan as the number of triangulations of a polygon by mean of nonintersecting diagonals. Stanley [13, 14] maintains a dynamic list of exercises related to Catalan numbers, including (at this date) 127 combinatorial interpretations. Closely related to Catalan numbers are ballot numbers. Their name...
متن کاملSome Properties of the Fuss–catalan Numbers
In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.
متن کاملFuss - Catalan Numbers in Noncommutative Probability
We prove that if p, r ∈ R, p ≥ 1 and 0 ≤ r ≤ p then the Fuss-Catalan sequence ( mp+r m ) r mp+r is positive definite. We study the family of the corresponding probability measures μ(p, r) on R from the point of view of noncommutative probability. For example, we prove that if 0 ≤ 2r ≤ p and r + 1 ≤ p then μ(p, r) is ⊞-infinitely divisible. As a by-product, we show that the sequence m m m! is po...
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In type A, the q, t-Fuß-Catalan numbers Cat (m) n (q, t) can be defined as a bigraded Hilbert series of a module associated to the symmetric group Sn. We generalize this construction to (finite) complex reflection groups and exhibit some nice conjectured algebraic and combinatorial properties of these polynomials in q and t. Finally, we present an idea how these polynomials could be related to ...
متن کاملq, t-FUSS-CATALAN NUMBERS FOR FINITE REFLECTION GROUPS
In type A, the q, t-Fuß-Catalan numbers can be defined as a bigraded Hilbert series of a module associated to the symmetric group. We generalize this construction to (finite) complex reflection groups and, based on computer experiments, we exhibit several conjectured algebraic and combinatorial properties of these polynomials with non-negative integer coefficients. We prove the conjectures for ...
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ژورنال
عنوان ژورنال: Journal of Probability and Statistics
سال: 2015
ISSN: 1687-952X,1687-9538
DOI: 10.1155/2015/482462