On the permanents of complements of the direct sum of identity matrices
On the permanents of complements of the direct sum of identity matrices
复制标题
关于单位矩阵直和的补集的常量
DOI：
10.1016/0196-8858(81)90001-4
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发表时间：
1981
影响因子：
1.1
通讯作者：
C. Mallows
中科院分区：
文献类型：
--
作者：
F. Chung;P. Diaconis;R. Graham;C. Mallows
一个用于测试超能力的经典实验有以下一般形式。一副扑克牌，由A张相同的i型1 i i i i r组成，洗牌后面朝下放置(在大多数这样的实验中，r= 5, A = 5 = 1 i i _(5)。然后，受试者尝试正确猜测每张牌的类型，因为这些牌是依次从牌组中取出的。在之前的工作中[2,3]，几位作者分析了允许各种反馈进入该过程的影响。例如，在每次猜错之后，受试者可能会被告知猜错的卡片实际上是什么。显然，如果使用得当，这些信息可以显著增加受试者在通过甲板时预期的正确猜测次数。考虑由25张牌组成的标准牌组，5种类型中每5张牌。在没有任何反馈（或ESP能力）的情况下，正确猜测的预期次数是5。有了完整的反馈，受试者可以期望获得超过8.64次的正确猜测，只需始终猜测剩余牌组中出现最频繁的类型（参见[3]）。b[3]研究的另一种非常重要的反馈类型是，受试者只被告知每次猜测是对还是错（但不知道猜错的卡片的正确身份）。使用这种部分反馈的最佳策略是极其复杂的，在某些情况下是反直觉的。例如，最优策略可能需要猜测剩余牌组中最不可能出现的类型（参见[3]）。这些研究中的一个基本量是N （A,，…）,,;b,,……， b,)，定义为u，+…的一副牌的排列次数。+ a,= n张牌，uj类型为i，使得符号1不出现在第一个b中，
A classic experiment used in testing for ESP abilities has the following general form. A deck of cards, consisting of a, identical cards of type i, 1 I i I r, is shuffled and placed face down (in most such experiments r= 5 and a,= 5 for 1 I i _ (5). The subject then attempts to correctly guess the type of each card as the cards are sequentially removed from the deck. In previous work [2, 3], several of the authors have analyzed the effects of allowing various kinds of feedback into this process. For example, after each incorrect guess the subject might be told what the guessed card actually was. Obviously such information, if used appropriately, could significantly increase the number of correct guesses the subject could expect to make during a pass through the deck. Consider the standard deck consisting of 25 cards, 5 cards of each of 5 types. Without any feedback (or ESP ability) the expected number of correct guesses is 5. With complete feedback, a subject can expect to achieve more than 8.64 correct guesses, simply by always guessing the most frequently occurring type in the remaining deck (see [3]). Another very important type of feedback, investigated in [3], was that in which the subject was just told whether each guess is right or wrong (but not the correct identity of an incorrectly guessed card). The optimal strategy for using this kind of partial feedback is extremely complex and, in some cases, counter-intuitive. For example, the optimal strategy can require guessing a type which is not the most likely type in the remaining deck (see [3]). A fundamental quantity in these studies is N (a,,..., a,; b,,..., b,) which is defined to be the number of arrangements of a deck of u,+...+ a,= n cards, with uj of type i, such that symbol 1 does not appear in the first b,