- 1.
- Each binomial tree is heap-ordered (key(x)
key(parent(x)).

This is the opposite of previous heap properties. - 2.
- There never exist two or more trees with the same degree in the heap.

A binomial heap with n nodes has at most binomial trees.

- n in binary =
<
*b*_{k},*b*_{k-1}, ..,*b*_{0}> bits

k = , n = - There is a one-to-one mapping between the binary representation and
binomial trees in a binomial heap.
- If
*b*_{i}= 1, then*B*_{i}is in the heap - Recall that there are 2
^{i}nodes in*B*_{i}

- At most + 1 bits are needed to express n base 2