Permutations with small maximal k-consecutive sums
نویسندگان
چکیده
منابع مشابه
Cards, permutations, and sums
We are given four cards, each containing four nonnegative real numbers, written one below the other, so that the sum of the numbers on each card is 1. We are allowed to put the cards in any order we like, then we write down the first number from the first card, the second number from the second card, the third number from the third card, and the fourth number from the fourth card, and we add th...
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In this paper we study the distribution of the number of occurrences of a permutation σ as a subword among all permutations in Sn. We solve the problem in several cases depending on the shape of σ by obtaining the corresponding bivariate exponential generating functions as solutions of certain linear differential equations with polynomial coefficients. Our method is based on the representation ...
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Finding the sub-vector with the largest sum in a sequence of n numbers is known as the maximum sum problem. Finding the k sub-vectors with the largest sums is a natural extension of this, and is known as the k maximal sums problem. In this paper we design an optimal O(n+k) time algorithm for the k maximal sums problem. We use this algorithm to obtain algorithms solving the two-dimensional k max...
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Wai Yan Pong ([email protected]) received his B.Sc. from the Chinese University of Hong Kong and his M.Sc. and Ph.D. from the University of Illinois at Chicago. He was a Doob Research Assistant Professor at the University of Illinois at Urbana-Champaign for three years. He then moved to California and is now teaching at California State University, Dominguez Hills. His research interests are in m...
متن کاملAvoiding consecutive patterns in permutations
The number of permutations that do not contain, as a factor (subword), a given set of permutations Π is studied. A new treatment of the case Π = {12 · · · k} is given and then some numerical data is presented for sets Π consisting of permutations of length at most 4. Some large sets of Wilf-equivalent permutations are also given.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.05.031