Why we can't create a binomial heap in max-heap format?
Why do you say that we cannot create a binomial max-heap?
Given any min-heap implementation you can always create its max version (and vice-versa).
An easy &quot;black-box&quot; way to see that this is true is considering what happens when all operations involving a key $k$ are actually performed on the key $-k$ instead.
That is, instead of inserting $k$ we insert $-k$; instead of deleting $k$ we delete $-k$; when we need to return the minimum key $k$, we return $-k$; etc...