منابع مشابه
Counting Inversions Adaptively
We give a simple and efficient algorithm for adaptively counting inversions in a sequence of n integers. Our algorithm runs in O(n+
متن کاملProof Trick : Small Inversions ∗
In the process of proving some goal . . .Hi : Ti . . . ` C, we often need to invert an hypothesis Hi. More precisely, if its type Ti is an instance I(a) of an inductive type family I(x), we want to select the only possible constructors for I(a) and to get the corresponding components. Common instances of this situation occur when reasoning on language operational semantics given in small-step o...
متن کاملJordan Geometries by Inversions
Jordan geometries are defined as spaces X equipped with point reflections Jxz a depending on triples of points (x, a, z), exchanging x and z and fixing a. In a similar way, symmetric spaces have been defined by Loos ([Lo69]) as spaces equipped with point reflections Sx fixing x, and therefore the theories of Jordan geometries and of symmetric spaces are closely related to each other – in order ...
متن کاملDecomposing Sets of Inversions
In this paper we consider the question how the set of inversions of a permutation π ∈ Sn can be partitioned into two subsets, which are themselves inversion sets of permutations in Sn. Our method is to study the modular decomposition of the inversion graph of π. A correspondence to the substitution decomposition of π is also given. Moreover, we consider the special case of multiplicative decomp...
متن کاملPermutations with Inversions
The number of inversions in a random permutation is a way to measure the extent to which the permutation is “out of order”. Let In(k) denote the number of permutations of length n with k inversions. This paper gives asymptotic formulae for the sequences {In+k(n), n = 1, 2, . . .} for fixed k.
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ژورنال
عنوان ژورنال: Trends in Ecology & Evolution
سال: 2019
ISSN: 0169-5347
DOI: 10.1016/j.tree.2018.12.005