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To quote from chapter VI section 2: ...There was no nice terminology for the subgroups $P _I$ with lie algebra the $\mathfrak p _I$ until R. Godement suggested calling them parabolic subgroups. …

A lot of sources mention that the adjective "tropical" is given in honor of Imre Simon, but it seems hard to find who precisely coined the term. I found some sources which attribute this to some Frenc …

I don't know if there is any better terminology but such families of sets (either disjoint or containing one another) are said to form a Laminar family or a hierarchical system. …

These are the Stirling numbers of the first kind. They enumerate, among other things, the number of permutations with a given number of cycles.

These unnamed numbers were famous enough to make it to A Mathematician's Apology. After mentioning what you wrote above Hardy writes: These are odd facts, very suitable for puzzle columns and like …

For a matroid the elements that are contained in every basis are called coloops, dual to the notion of a loop, which is an element not contained in any basis. Since you are interested in linearly inde …

The evaluation of your sequence is equivalent to the evaluation of certain weighted sums over binary trees. The resulting identities are often called hook length formulas. Suppose $\mathcal B_n$ denot …

The same terminology is used for edges. You will find that there is a lot of literature on the problem of constructing large sets of pseudosimilar vertices or edges. … Unfortunately searching for "similar vertices" is more likely to bring up results that are more devoted to pseudosimilarity, so it's not very efficient for your goal, but it does seem to be the most common terminology …

This inequality is essentially equivalent to the Classical isoperimetric inequality. If you have a measurable body $X$ in $\mathbb{R}^n$ and a ball $B\subset \mathbb R^n$ of same volume then you have …

This suggests the terminology "$v$ to $H$ expansion", and then you could define "$H$ to $v$ contraction" similarly (unfortunately I don't think this is standard). …