منابع مشابه
Sorting and Selecting in Totally Monotone
An mn matrix A is called totally monotone if for all i1 < i2 and j1 < j2, Ai1; j1] > Ai1; j2] implies Ai2; j1] > Ai2; j2]. We consider the complexity of comparison-based selection and sorting algorithms in such matrices. Although our selection algorithm counts only comparisons its advantage on all previous work is that it can also handle selection of elements of diierent (and arbitrary) ranks i...
متن کاملSet Sequences and Monotone Class
In this paper we first defined the partial-union sequence, the partial-intersection sequence, and the partial-difference-union sequence of given sequence of subsets, and then proved the additive theorem of infinite sequences and sub-additive theorem of finite sequences for probability. Further, we defined the monotone class of families of subsets, and discussed the relations between the monoton...
متن کاملSorting Operators for Finite Sequences
(Def. 1)(i) If len f = 0, then maxp f = 0, and (ii) if len f > 0, then maxp f ∈ dom f and for every natural number i and for all real numbers r1, r2 such that i∈ dom f and r1 = f (i) and r2 = f (maxp f ) holds r1 ≤ r2 and for every natural number j such that j ∈ dom f and f ( j) = f (maxp f ) holds maxp f ≤ j. Let f be a finite sequence of elements of R. The functor minp f yields a natural numb...
متن کاملOn the number of monotone sequences
One of the most classical results in Ramsey theory is the theorem of Erdős and Szekeres from 1935, which says that every sequence of more than k numbers contains a monotone subsequence of length k + 1. We address the following natural question motivated by this result: Given integers k and n with n > k + 1, how many monotone subsequences of length k + 1 must every sequence of n numbers contain?...
متن کاملCompletely Monotone Sequences and Universally Prestarlike Functions
We introduce universally convex, starlike and prestarlike functions in the slit domain C \ [1,∞), and show that there exists a very close link to completely monotone sequences and Pick functions.
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ژورنال
عنوان ژورنال: Information and Computation
سال: 1994
ISSN: 0890-5401
DOI: 10.1006/inco.1994.1050