Which core exercises should I avoid after tummy tuck?

I ask patients to avoid exercises that target the abdominal muscles for 6 weeks and then gradually progress until full activity is regained at 12 weeks.

It sounds like you are a very active person devoted to excellent physical condition.  All of the exercises that you have listed will likely impact on your core to some degree.  In order for you to have the best long-term result it is best to strictly follow the recommendations given to you by your surgeon.  Good luck on your upcoming triathlon.

Best to follow the recommendations of your plastic surgeon since he knows your surgical procedure.  In my practice I allow patients to resume all vigorous activities at 6 - 8  weeks.  

I have the greatest restriction of core strengthening exercises against resistance for 6-8 weeks.  Then they can gradually exercise and strengthen them over the next few months.  It is important to fully discuss and work with your plastic surgeon safe exercises for you.  Your surgeon will best know what his procedure had done and how to achieve optimal scars of the skin and tightening to achieve a flat abdomen.

My personal answer may differ from your surgeon's, and your individual circumstances may require a different programme than what I generally recommend. Because  you are a competitive athlete, you should see your doctor for specific guidance.However the first point to understand  ( and you probably know this already) is that all your muscles are linked, and especially those of your core. To effectively use your legs you must have a stable core; to box effectively, you move from the core. Your recti and your obliques are attached to each other. Nothing is truly isolated.Having said that, I normally recommend patients start doing crunches, planks, and other core exercises  at six weeks post op, to work up in terms of intensity and resistance gradually, and to back off with anything that hurts. If you have had problems such as a seroma, this timing needs to be adjusted accordingly. Some patients are already doing some core work outs by 4 weeks, and  although  I don't generally recommend this, if they had a simple uncomplicated recovery there is rarely an issue.Again, ask your own surgeon. Good luck!