A stack is an operation where x is y-tated (raised by y arrows to y to y arrows to y to y arrows.... to y and so on for n times) to itself , usually expressed in arrow notation (hence "y arrows"). A stack expression is an expression where there is only stacks, and the verb stack respectively is to "raise by y arrows to y to y arrows to y to y arrows.... to y and so on for n times". There are rules on what is a stack and what is not, that are: 1. A stack only has 2 values, x and y or any pair of variables/values respectively (for regular numerical values, you must know which is x (base) and y —hyperoperator), 2. For any type n-omino, y must be stacked by n times, 3. For any type n-stack, stacks must be repeated n times, 4. x cannot appear as a hyper-operator, and y cannot appear as a base, unless x = y. These are the rules to help to determine which expression is a stack or not, and must be used to see if a proclaimed stack is actually a stack (extra info at the near-end of the page which helps determine which stack is a proper stack).

A basic stack is as defined as follows:

Here are the types of stacks, which represent how many stacks are there in an expression.

• Monostack - Only 1 stack, 

• Distack - 2 stacks, 

• Tristack - 3 stacks, eg.

And the rest should be easily self-explained (tetrastack, pentastack, hexastack, etc..).
However, there are other sub-types of stacks where y is also stacked y times, most of which are named by polyominoes.

• Monomino Stack - where y is stacked by y for 1 times,

• Domino Stack - where y is stacked by y for 2 times, eg.

• Tromino/Triomino Stack - where y is stacked by y for 3 times,

• Tetromino Stack - where y is stacked by y for 4 times, 

And with that, the rest should be also self-explained, since other n-ominoes can be defined using other geometric polyominoes' names (eg. Pentomino, Hexomino, etc.)

What can be a stack:

Here are examples on what stack expression is considered proper:

↑ equation above is a called a complex stack—we'll get to that in another article .

Stacks in other notations

Since I have defined stacks only respectively in arrow notation, here are stacks in other notations (the presence of errors and mistakes may be guaranteed, be wary).

Square Bracket Notation

[more will be added soon to this section]

Names of various stack expressions

(name for goes as: subtype - type)

[also continuing this sooner or later]

Googology

Stacks can be used to make or find googolisms, though it will probably remained Ill-defined or remain inferior to other concepts and ideas. Soon I will make a notation to simplify stacks, for the sake of new googolisms, and I must spend at least 1 week trying to perfect it.

Comments~

• As said, I'll be making a notation sooner or later to easily represent expression with stacks.

• The "Hyper-Operator Function/Notation" thing came from Wikipedia, pls help me find the actual name of the thing for the sake of uhh.. sophistication? -got removed anyways-

• Final Comment, the expectancy of the presence of errors, misconceptions, and mistakes in this article is signficant,.