What is the symbol “between” (≬) used for?

I found it in the Journal of Combinatorial Optimization (2007) 13:217-221, February 14, 2007: A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. There the expression \{<,\between\} has been used, as can be seen in the abstract.

Regarding intervals, \between may stand for a crossing/overlapping relation like < for a precedence order and kind of a subset symbol for inclusion/nesting. See also Extracting constrained 2-interval subsets in 2-interval sets.

In such difficult cases, the LaTeX search engine of Springer is a useful tool.

It is not new. It appears on page 28 of "Kummer's quartic surface" by R W H T Hudson (Cambridge University Press 1905, republished 1990; WorldCat) without explanation, so was presumably well understood by Projective Geometrists then.

It was used by Hudson in "Kummer's Quartic Surface" to denote the inner product of two single-row matrices, for instance (a,b,c,d≬x,y,z,t) = ax+by+cz+dt. The advantage of the notation seems slight and may merely have saved space by not having to write the second matrix as a vertical column in the usual way.