论文标题
生根的平面图和广义战鱼之间的培训
A bijection between rooted planar maps and generalized fighting fish
论文作者
论文摘要
战鱼类别是最近引入的分支表面的模型，使平行四边形多支着平行四边形。我们也可以将它们视为细胞的粘合物，在限制在象限或堤防单词的象限或洗牌的方格上行走。从这些不同的角度来看，我们引入了一种自然的战鱼的延伸，我们称之为\ emph {广义战鱼}。我们表明，普遍的战鱼正是植根于平面地图的Mullin代码，并具有其独特的最右边的搜索跨越树（也称为Lehman-Lenormand code）。特别是，这种对应关系给出了战斗鱼与不可分割的根平面图之间的两次射击，从而丰富了由序列$ \ frac {2} {（n+1）（2N+1）} \ binom {3n} {n} $的序列$ \ frac {2} {（n+1）{（n+1）{（n+1）{n} $的物体{2} {（n+1）} $。
The class of fighting fish is a recently introduced model of branching surfaces generalizing parallelogram polyominoes. We can alternatively see them as gluings of cells, walks on the square lattice confined to the quadrant or shuffle of Dyck words. With these different points of view, we introduce a natural extension of fighting fish that we call \emph{generalized fighting fish}. We show that generalized fighting fish are exactly the Mullin codes of rooted planar maps endowed with their unique rightmost depth-first search spanning tree, also known as Lehman-Lenormand code. In particular, this correspondence gives a bijection between fighting fish and nonseparable rooted planar maps, enriching the garden of bijections between classes of objects enumerated by the sequence $\frac{2}{(n+1)(2n+1)} \binom{3n}{n}$.
