I am reading an article about counting hexagonal p-minos (the article is in a combinatorics book) and I saw a notation I don't understand:
$0>(a,b)>-p$ .
$a,b,p$ are integers and so ">" means 'bigger', but what can be the meaning of "$(a,b)$" ?
I am reading an article about counting hexagonal p-minos (the article is in a combinatorics book) and I saw a notation I don't understand:
$0>(a,b)>-p$ .
$a,b,p$ are integers and so ">" means 'bigger', but what can be the meaning of "$(a,b)$" ?
From the comments it seems pretty clear that it means $0>a>-p$ and $0>b>-p$ (and also that $a$ and $b$ should be a' and b' respectively). The notation is awful, but I think I know why the author doesn't write $0>a,b>-p$: that can be easily misread as $0>a$, $b>-p$, which is a much weaker condition (look closely, if like me you don't see any difference, right-click on the formulas to see the TeX source). I regularly have difficulty avoiding this kind of ambiguity when writing; one could promise to the reader to never to write two conditions separated by just a comma that means "and", but that is an annoying constraint as well, in situations where one needs a somewhat complicated set like $\{(x,y)\in\mathbb R^2\mid x\geq 1, 0\leq y\leq x^2\}$ (not all readers are used to "$\land$" meaning "and"; by the way the perversion of writing "$(a,b)$" instead of "$\gcd(a,b)$" also sometimes takes the alternative form of writing it "$a\land b$"; ah, the delights of laziness…).
It is true that with his private notation the author has managed to make clear that he does not mean $0>a$ and $b>-p$, but at the price of totally obfuscating what he does mean, and all that to save a few keystrokes.