Hey everyone, I've been interested in large numbers for a long time and I am really excited to discover this wiki for the first time. After I saw all these mind-blowing fast-growing functions on your site I just HAD to create my own! :D So would you mind having a look at my notation? It's called **Super-Lambda Array Notation**, a new array notation I invented that I think goes beyond the power of ExE, BEAF, and HAN. I'm kinda new at this googology stuff, so feedback is welcome :P In making this notation I tried to start from the ground up and find ways to strengthen the notation on every level. The notation has the following rules:

- Every expression must start with Λ (capital Greek lambda).
- Expressions can contain any list of numbers.
- Λn = n^n
- Λ#,1 = Λ# where # denotes rest of array.
- Λn,# = Λ(Λn),#-1
- Λa,b,# = Λ(Λ(...(b times)...Λ(a,Λ(a,Λ(a,Λ(a,...)...)...(b times)...)...#)...#)...#)

This is only the first level of SLAN, but already it is powerful than 2-entry arrays in ExE, BEAF, and HAN. Notice how in the last rule the list gets recursed over in *both arguments*. This results in amazingly, catastrophically larger numbers than any other 2-argument notation I've seen! I think the growth rate is f_w but I'm not too good at the FGH stuff, I'll leave it for other people to prove. Another distinguishing property of Super-Lambda Array Notation concerns the use of Greek letters instead of ordinary English and ASCII letters. Anyways, we can move on to the extension, **Extended Super-Lambda Array Notation** (ESLAN):

- At some point in the expression we can have a
**jump-marker**Γ (Greek capital gamma). - Let @ represent the expression up to the jump-marker, and # is the rest of the expression.
- Λ1Γ# = 1
- ΛnΓ# = Λn-1Γ(Λn-1Γ(Λn-1Γ(...(b times)...Λn-1#)))
- Λa,b,@Γ# = Λ(@Λ(@...(b times)...Λ(@a,Λ(@a,Λ(@a,Λ(@a,...)...)...(b times)...)...#)...#)...#)

With only five simple rules I think this extends Super-Lambda Array Notation to reach a strength level of f_w^2! To extend to higher-level notations we need to introduce more dimensional notations, which brings us to **Hyper-Dimensional Mega-Extended Super-Lambda Array Notation** (whew, that's a long name :P):

- We use Γ2 for a
**double jump-marker**, which means a second-dimensional break. - Γ3 is the
**triple jump-marker**, and so on. ΓΓ is the**jump-jump marker**, Γ^3 the**jump-jump-jump marker**or jump-3 marker, and so on to jump^jump markers, jump^^^jump markers, Λ(jump,jump) markers, ........ We call these all**jump-structures**. - The
**accumulator entry**in an X-tuple jump-structure is the X-1th entry. The accumulator in a jump-jump marker is the bth entry (when solving rule 5 above), for a jump-jump-jump marker it's the Λb'th entry, and so on for other jump-structure markers. - The three simple rules are:
- Λn = n^n
- Λ1Δ@ = Λ@ where Δ is any jump-structure-marker
- Λ#Δ@ = Λ#Δ(Λ#Δ(Λ#Δ@(Λ#Δ...))) (b times, where b is the value of the accumulator entry and Δ is a jump-structure marker)

And of course we can define all sorts of numbers. I define **Dave's Number** as ΛgoogolΔgoogol where Δ is a ΛjumpΔjump marker where Δ is a ΛjumpΔjump marker where Δ is a ΛjumpΔjump marker where ... a total of googol times! *Yikes!!!!!* I think this notation is SO strong that it might be beyond any known ordinal notation... I have NO idea what it could be in FGH! I'm wondering if you have any idea what it would be. Still a work in progress, and there may be some things that aren't well-defined, but I hope you can sort this all out :P Maybe someone can make an article about this? I think it's quite a novel discovery in googology and might deserve an article in the wiki! Thanks in advance!