Can I use map, fold, filter in publications? I have to write down algorithms in my thesis, and these are getting way shorter if I use "map," "fold," and "filter" heavily.

This generally results in a "map, fold, filter"-chain with a depth of 3.

Structure: 

fold( map( ..., filter(...))...)


Is it okay to assume that these functions are known, and what is the parameter convention?
If you are writing to a computer science audience who would be expected to have a some knowledge of functional programming, then yes, these sorts of basic elements are quite reasonable to assume knowledge of.

If you are writing to an audience without such background knowledge, then you will need to explain what they are (and give a reference for more information) before you use them.