Consider a max heap tree with $100$ elements and a node from the same level is chosen randomly among all valid balanced heap trees with $n$ nodes. What is the probability that it is the $36^\text{th}$ smallest element______ .
My attempt:
(Please, find definition of Binary Heap on Wiki: https...
In number theory, the specialty additive number theory studies subsets of integers and their behavior under addition. More abstractly, the field of "additive number theory" includes the study of abelian groups and commutative semigroups with an operation of addition. Additive number theory has close ties to combinatorial number theory and the geometry of numbers. Two principal objects of study are the sumset of two subsets A and B of elements from an abelian group G,
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In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
== Scope ==
Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations (addition, subtraction, multiplication, and division). Additive combinatorics is the special case when only the operations of addition and subtraction are involved.
Arithmetic combinatorics is explained in Green's review of "Additive Combinatorics" by Tao and Vu.
== Important results ==
=== Szemerédi's theorem ===
Szemerédi's theorem is ...
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Here is my attempt to prove the Well-ordering principle, i.e. Any non-empty subset of $\Bbb N$, the set of natural numbers has a minimum element.
Proof: Suppose there exists a non-empty subset $S$ of $\Bbb N$ such that $S$ has NO minimum element.
Define $A = \left\{n\in \Bbb N : (\forall s\in S...
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