Results 11 to 20 of about 45 (45)
Cosine polynomials with few zeros
Bulletin of the London Mathematical Society, Volume 53, Issue 3, Page 877-892, June 2021., 2021 Abstract In a celebrated paper, Borwein, Erdélyi, Ferguson and Lockhart constructed cosine polynomials of the form fA(x)=∑a∈Acos(ax),with A⊆N, |A|=n and as few as n5/6+o(1) zeros in [0,2π], thereby disproving an old conjecture of Littlewood. Here we give a sharp analysis of their constructions and, as a result, prove that there exist examples with as ...
Tomas Juškevičius, Julian Sahasrabudhe
wiley +1 more source
EXPECTED MEAN WIDTH OF THE RANDOMIZED INTEGER CONVEX HULL
Mathematika, Volume 67, Issue 2, Page 422-433, April 2021., 2021 Abstract Let K⊂Rd be a convex body, and assume that L is a randomly rotated and shifted integer lattice. Let KL be the convex hull of the (random) points K∩L. The mean width W(KL) of KL is investigated. The asymptotic order of the mean width difference W(λK)−W((λK)L) is maximized by the order obtained by polytopes and minimized by the order for smooth ...
Binh Hong Ngoc, Matthias Reitzner
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Discrete Mathematics & Theoretical Computer Science, 2007 Let a and b be two positive integers. A culminating path is a path of Z^2 that starts from (0,0), consists of steps (1,a) and (1,-b), stays above the x-axis and ends at the highest ordinate it ever reaches.
Mireille Bousquet-Mélou, Yann Ponty
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A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
Forum of Mathematics, Sigma, 2019 Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of $n$ without $k$ consecutive parts.
DANIEL M. KANE, ROBERT C. RHOADES
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The distribution of m-ary search trees generated by van der Corput sequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 We study the structure of $m$-ary search trees generated by the van der Corput sequences. The height of the tree is calculated and a generating function approach shows that the distribution of the depths of the nodes is asymptotically normal ...
Wolfgang Steiner
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Extended Fibonacci numbers and polynomials with probability applications
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 50, Page 2681-2693, 2004., 2004 The extended Fibonacci sequence of numbers and polynomials is introduced and studied. The generating function, recurrence relations, an expansion in terms of multinomial coefficients, and several properties of the extended Fibonacci numbers and polynomials are obtained.
Demetrios L. Antzoulakos
wiley +1 more source
Forum of Mathematics, Pi, 2016 We prove that proper coloring distinguishes between block factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently well-separated locations are independent; it is a block factor if it ...
ALEXANDER E. HOLROYD, THOMAS M. LIGGETT
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On the birthday problem: some generalizations and applications
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 60, Page 3827-3840, 2003., 2003 We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functions U(−; −; −) which are computable using the software Mathematica.
P. N. Rathie, P. Zörnig
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Generalized distributions of order k associated with success runs in Bernoulli trials
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 13, Page 801-815, 2003., 2003 In a sequence of independent Bernoulli trials, by counting multidimensional lattice paths in order to compute the probability of a first‐passage event, we derive and study a generalized negative binomial distribution of order k, type I, which extends to distributions of order k, the generalized negative binomial distribution of Jain and Consul (1971 ...
Gregory A. Tripsiannis +2 more
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A zero‐inflated occupancy distribution: exact results and Poisson convergence
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 28, Page 1771-1782, 2003., 2003 We introduce the generalized zero‐inflated allocation scheme of placing n labeled balls into N labeled cells. We study the asymptotic behavior of the number of empty cells when (n, N) belongs to the “right” and “left” domain of attraction. An application to the estimation of characteristics of agreement among a set of raters which independently ...
Nikolai Kolev, Ljuben Mutafchiev
wiley +1 more source