bijective proof problems 中的一些生草评论

x义x · 2020-12-16 16:02:09 · 个人记录

开幕雷击：

For those wanting to plunge（突然向前冲） immediately into serious research, the most interesting open bijections (but most of which are likely to be quite difficult) are Problems 27, 28, 59, 107, 143, 118, 123 (injection of the type described), 125, 140, 148, 151, 195, 198, 215, 216, 217, 226, 235, and 247.

接下来几乎都是对 [*] 难度的题目（未知是否存在双射证明）的评论。有些是对题目的 unsolved 扩展的评论。

I’m not sure, however, whether anyone has given a direct bijective proof of (2).
A bijective proof would be of great interest.
None of these six pairs is known to be equal by a bijective proof!
In this case a bijective proof is unknown (and probably impossible).
This is one of the most intriguing（引人入胜的） open problems in the area of bijective proofs.
Several bijective proofs are known, but none are really satisfactory. What is wanted is a “direct” bijection whose inverse is easy to describe.
Any bijective proof of this difficult result would be an impressive achievement.

对 [3] 级题也有一些奇妙的评论。