论文标题
关于“发现它！”的存在不是投影飞机的甲板
On the existence of "Spot It!" decks that are not projective planes
论文作者
论文摘要
游戏“发现它！”播放一张牌，每双纸牌都有一个匹配的符号，目的是找到比赛中最快的符号。众所周知，有限的投影平面对应于每张卡中包含$ n $符号的甲板，并且每个符号都出现在$ n $卡上。在本文中，我们放宽了出现符号的卡数量的假设：我们研究对称甲板，其中每个符号出现与次数相同的次数，并介绍了最大甲板的概念，为甲板提供了具有此属性的足够条件。我们还制作了各种有趣的甲板的例子，这些甲板与投影平面无关。
The game "Spot It!" is played with a deck of cards in which every pair of cards has exactly one matching symbol and the aim is to be the fastest at finding the match. It is known that finite projective planes correspond to decks in which every card contains $n$ symbols and every symbol appears on $n$ cards. In this paper we relax the hypothesis on the number of cards on which a symbol appears: we study symmetric decks in which every symbol appears the same number of times and we introduce the concept of maximal deck, providing a sufficient condition for a deck to have this property. We also produce various examples of interesting decks which do not correspond to projective planes.
