Can a MacBook Air support 2560x1600 output via HDMI using a Mini DisplayPort/Thunderbolt to HMDI adaptor?
I own a 2013 MacBook Air.  This is equipped with a Thunderbolt 1 port :

Mini-DisplayPort -&gt; HDMI adapter (1920x1200 max.)

Mini-DisplayPort -&gt; DisplayPort adapter (upto 2560x1600 max.)

I've used both and am now driving daily on my MBA 13" with a monitor running at 2560x1440.