منابع مشابه
A Sequence of Unimodal Polynomials
A finite sequence of real numbers {d0, d1, · · · , dm} is said to be unimodal if there exists an index 0 ≤ j ≤ m such that d0 ≤ d1 ≤ · · · ≤ dj and dj ≥ dj+1 ≥ · · · ≥ dm. A polynomial is said to be unimodal if its sequence of coefficients is unimodal. The sequence {d0, d1, · · · , dm} with dj ≥ 0 is said to be logarithmically concave (or log concave for short) if dj+1dj−1 ≤ dj for 1 ≤ j ≤ m − ...
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Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.
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We present a general result that, using the theory of symmetric functions, produces several new classes of symmetric unimodal polynomials. The result has applications to enumerative combinatorics including the proof of a conjecture by R. Stanley.
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The estimation of probability density functions is one of the fundamental aspects of any statistical inference. Many data analyses are based on an assumed family of parametric models, which are known to be unimodal (e.g., exponential family, etc.). Often a histogram suggests the unimodality of the underlying density function. Parametric assumptions, however, may not be adequate for many inferen...
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Let g(X) ∈ K(t1, . . . , tm)[X] be a generic polynomial for a group G in the sense that every Galois extension N/L of infinite fields with group G and K ≤ L is given by a specialization of g(X). We prove that then also every Galois extension whose group is a subgroup of G is given in this way. Let K be a field and G a finite group. Let us call a monic, separable polynomial g(t1, . . . , tm, X) ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.06.010