we will re-enact the story of proving a conjecture by anders claesson and svante linusson. along the way, we are naturally led to a particular bijection between matchings and permutations; however, this bijection is somewhat flawed. we will discover a general technique to circumvent these flaws, leading to a new bijection that completes the proof. time permitting, we will also use this technique to prove a recent conjecture by miles jones and jeffrey remmel. this talk should be accessible to graduate 2022年亚洲世界杯预选赛 of all areas of math.