First, we study its sensitivity to various string operations. We show that chi cannot increase by more than 2 after appending or prepending a character to the string. As a consequence, we are able to give simple linear-time online algorithms to compute smallest suffixient sets. We also show that, although reversing the string can increase chi by an arbitrary O(n) value, it always holds chi(T)/chi(T^R) <= 2. We also prove lower and upper bounds for the additive or multiplicative increase of chi after applying arbitrary edit operations, or rotating the text. In particular, we show that the additive increase can be as large as Omega(sqrt(n)) for all those operations.
Secondly, we place chi among known repetitiveness measures. In particular, we show chi <= 2r (where r is the number of runs in the Burrows-Wheeler Transform of the string), that there are string families where chi=o(v) (where v is the size of the smallest lexicographic parse of the string), and that chi is uncomparable to almost all reachable measures based on copy-paste mechanisms. In passing, we give precise bounds for chi for some relevant string families, for example chi <= sigma+2 on episturmian words over alphabets of size sigma (e.g., chi <= 4 on Fibonacci strings, for which we precisely characterize the only two smallest suffixient sets).