a) Start and end with a number
b) Hyphen should start and end with a number
c) Comma should start and end with a number
d) Range of number should be from 1-31
The other approaches have not restricted the allowed range of numbers. This allows 1 through 31 only, and seems simpler than some of the monstrosities people have come up with ...
^([12][0-9]?|3[01]?|[4-9])([-,]([12][0-9]?|3[01]?|[4-9]))*$
There is no check for sensible ranges; adding that would make the expression significantly more complex. In the end you might be better off with a simpler regex and implementing sanity checks in code.