Proof of a conjecture on unimodality
Proof of a conjecture on unimodality
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DOI：
10.1016/j.ejc.2004.04.012
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发表时间：
2005-07
期刊：
影响因子：
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通讯作者：
Yi Wang;Y. Yeh
中科院分区：
文献类型：
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作者：
Yi Wang;Y. Yeh
设P(x)为m次多项式，系数非负且非递减。我们证明了对于任意正实数d， P（x+d）的系数形成一个单峰序列的猜想，其中d为正整数的特殊情况在以前的工作中已经得到了证明。进一步探讨了P（x+d）的模态的位置，给出了P（x+d）在m和d上具有唯一模态≤m−d≤d+1的几个充分条件。
Let P(x) be a polynomial of degree m, with nonnegative and nondecreasing coefficients. We settle the conjecture that for any positive real number d, the coefficients of P(x+d) form a unimodal sequence, of which the special case d being a positive integer has already been asserted in a previous work. Further, we explore the location of modes of P(x+d) and present some sufficient conditions on m and d for which P(x+d) has the unique mode ⌈ m−d d+1 ⌉ .