Bijections between planar maps and planar linear normal λ-terms with connectivity condition
Wenjie Fang
线性λ-term的枚举最近引起了相当多的关注,部分原因是它们与组合图的联系。 Zeilberger和Giorgetti(2015)在平面线性正 λ-terms 和平面图之间进行了递归双击,当限制为2个连接的λ-terms(即没有封闭的子术语)时,会导致无桥平面图。 受此限制的启发,Zeilberger和Reed(2019)推测,3连接的平面线性正常λ-terms与双部分平面图具有相同的计数公式。 在这篇文章中,我们通过在这两个家庭之间进行直接的争吵来解决这个猜想。 此外,使用类似的方法,我们在平面线性正态λ-terms和平面图之间给出直接的双子,其限制为2连接的λ-term导致无环平面图。 这种双击似乎与Zeilberger和Giorgetti不同,即使在采取地图双重之后。 我们还探讨了我们的双击的列举后果。
The enumeration of linear λ-terms has attracted quite some attention recently, partly due to their link to combinatorial maps. Zeilberger and Giorgetti (2015) gave a recursive bijection between planar linear normal λ-terms and planar maps, which, when restricted to 2-connected λ-terms (i.e., without closed sub-terms), leads to bridgeless planar maps. Inspired by this restriction, Zeilberger and Reed (2019) conjectured that 3-connected planar linear normal λ-terms have the same counting formula a...
