I had to look it up, never heard of it either.
https://www.mlb.com/cut4/reds-wear-sleeveless-1956-throwback-jerseys
1956 Road - One of the most iconic uniforms in Reds history, the one-year style worn by the 1956 Reds coincided with one of the most memorable seasons in franchise history. That season, a strong contingent of Reds hitters led by Ted Kluszewski, Wally Post, Gus Bell and rookie Frank Robinson helped the club tie the then-Major League record for home runs by a team with 221. The slugging Reds were the talk of baseball as the club's powerful bats kept the team in pennant contention into the season's final week. The vest-style uniform was a first for the Reds and its adoption was inspired in part by the bulging biceps of "Big Klu," the club's intimidating first baseman. The uniform also marked the first and only time that the club's Mr. Redlegs mascot appeared on the front of the team's jerseys.
Did baseball players actully wear no-sleeve jerseys back in the day? I've never seen one before.