Preapring for going live.HEADmaster

 Changes to be committed:
        modified:   .gitignore
        modified:   content/about.md
        new file:   content/posts/Generating Functions.md
        new file:   content/posts/Void Linux - A Comfy Guide.md
        modified:   content/posts/_index.md
        renamed:    content/posts/code_test.md -> content/posts/code-syntax-highlighting.md
        deleted:    content/posts/some_cool_stuff.md
        modified:   content/posts/typography.md
        new file:   content/posts/youtube.md
        renamed:    content/posts/How I made this Blog with Zola.md -> content/posts/zola-blog.md
        modified:   static/Alphara.png

11 files changed, 134 insertions, 54 deletions

diff --git a/.gitignore b/.gitignore
index 364fdec..4f18294 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1 +1,2 @@
 public/
+.obsidian/
diff --git a/content/about.md b/content/about.md
index 85c6e79..e9eda42 100644
--- a/content/about.md
+++ b/content/about.md
@@ -1,9 +1,4 @@
 +++
 title = "About"
+date = 2025-01-27
 +++
-
-Hi there! My name is Iustin. I'm a math student from Romania with a background in AI development and research. This blog represents my attempt at sharing personal thoughts and experiences as a follow-through venture in AI research, mathematics, philosophy and Linux related things, as well as a bunch of other things that define my interests.
-
-I wish to write interesting, useful, qualitative and fun content for you to read and learn from. I hope you will enjoy!
-
-Welcome to my corner of organised anarchy on the internet! Feel free to reach out to me if you have any questions or comments or would like to chat. I am always happy and open to meet passionate people.
diff --git a/content/posts/Generating Functions.md b/content/posts/Generating Functions.md
new file mode 100644
index 0000000..8d90696
--- /dev/null
+++ b/content/posts/Generating Functions.md
@@ -0,0 +1,53 @@
++++
+title = "Generating Functions"
+date = 2024-10-08
+draft = true
+
+[taxonomies]
+tags = ["math"]
+
+[extra]
+math = true
+disable_comments = true
+toc = false
++++
+
+A generating function is just a different way of writing a sequence of numbers. Here we will be dealing mainly with sequences of numbers $(a_n)$ which represent the number of objects of size $n$ for an enumeration problem. The interest of this notation is that certain natural operations on generating functions lead to powerful methods for dealing with recurrences on $a_n$.
+
+***Theorem 1:*** Let $(a_n)_{n \geq 0}$ be a sequence of numbers. The generating function associated to this sequence is the series:
+
+$$A(x) = \sum_{n \geq 0} a_n x^n .$$
+
+Also if we consider a class $A$ of objects to be enumerated, we call generating function of this class the generating function
+
+$$A(x) = \sum_{n \geq 0} a_n x^n ,$$
+
+where $a_n$ is the number of objects of size $n$ in the class.
+
+Note that the variable $x$ in generating functions doesn’t stand for anything but serves as a placeholder for keeping track of the coefficients of $x^n$.
+
+**Example 1:** The generating function associated to the class of binary sequences (where the size of a sequence is its length) is $A(x) = \sum_{n \geq 0} 2^n x^n$ since there are $a_n = 2^n$ binary sequences of size $n$.
+
+**Example 2:** Let $p$ be a positive integer. The generating function associated to the sequence $a_n = \binom{k}{n}$ for $n \leq k$ and $a_n = 0$ for $n > k$ is actually a polynomial:
+
+$$A(x) = \sum_{n \geq 0} \binom{k}{n} x^n = (1 + x)^k .$$
+
+Here the second equality uses the binomial theorem. Thus $A(x) = (1+x)^k$ is the generating function of the subsets of $\set{1, 2, \ldots, k}$ (where the size of a subset is its number of elements).
+
+We see on this second example that the generating function has a very simple form. In fact, more simple than the sequence itself. This is the first magic of generating functions: in many natural instances the generating function turns out to be very simple.
+
+Let us now modify this example in connection with probabilities. Suppose we have a coin having probability $p$ of landing on heads and a probability $q = 1 - p$ of landing on tails. We toss it $k$ times and denote by an the probability of getting exactly $n$ heads. What is the generating function of the sequence $(a_n)$? Well, it can be seen that $a_n = \binom{k}{n} q^{k-n} p^n$ thus the generating function is
+
+$$A(x) = \sum_{n \geq 0} \binom{k}{n} q^{k-n} p^n x^n = (q + px)^k .$$
+
+using the binomial theorem again.
+
+Now, we observe that the generating function is
+
+$$(q + px)(q + px)(q + px)\cdot\cdot\cdot(q + px) ,$$
+
+which is just multiplying $k$ times the generating function $(q + px)$ corresponding to a single toss of the coin.
+
+This is the second magic of generating functions: the generating function for complicated things can be obtained from the generating function for simple things. We will explain this in details, but first we consider an example.
+
+***Theorem 2:*** Let $\mathcal{A}$ and $\mathcal{B}$ be classes of objects and let $A(x)$ and $B(x)$ be their generating functions. Then the class $\mathcal{C} = \mathcal{A} \times \mathcal{B}$ has generating function $C(x) = A(x)B(x)$.
diff --git a/content/posts/Void Linux - A Comfy Guide.md b/content/posts/Void Linux - A Comfy Guide.md
new file mode 100644
index 0000000..3e40e6d
--- /dev/null
+++ b/content/posts/Void Linux - A Comfy Guide.md
@@ -0,0 +1,16 @@
++++
+title = "Void Linux - A Comfy Guide"
+date = 2024-10-08
+draft = true
+
+[taxonomies]
+tags = ["linux", "guide"]
+
+[extra]
+disable_comments = true
+toc = false
++++
+
+I've been using Void Linux for about 4 years now (4th Feb 2021 -> 8th Oct 2024), and I've been loving it. It's a rolling release distribution that's simple, fast, and lightweight. It's a great choice for those who want to learn more about Linux, or for those who want to have a system that's easy to maintain and customize.
+
+Void Linux has been, in my experience, my go-to choice in
diff --git a/content/posts/_index.md b/content/posts/_index.md
index b33cac7..ca4530f 100644
--- a/content/posts/_index.md
+++ b/content/posts/_index.md
@@ -1,4 +1,4 @@
 +++
 title = "Posts"
 sort_by = "date"
-+++
++++
\ No newline at end of file
diff --git a/content/posts/code_test.md b/content/posts/code-syntax-highlighting.md
index ed248f9..7df307d 100644
--- a/content/posts/code_test.md
+++ b/content/posts/code-syntax-highlighting.md
@@ -1,23 +1,23 @@
 +++
-title = "Test code syntax highlight"
-date = 2020-10-13
+title = "Test Code Syntax Highlighting"
+date = 2025-01-27
 draft = false
 
 [taxonomies]
-tags = ["test", "code"]
+tags = ["test-formatting"]
 
 [extra]
 disable_comments = false
-permalink = "https://alphara.art/posts/code-test/"
+permalink = "https://alphara.art/posts/code-syntax-highlighting/"
 toc = false
 
 [extra.earlier]
-title = "Typography"
+title = "Test Typography"
 permalink = "https://alphara.art/posts/typography/"
 
 [extra.later]
-title = "Henlo Internet!"
-permalink = "https://alphara.art/posts/how-i-made-this-blog-with-zola/"
+title = "Test YouTube"
+permalink = "https://alphara.art/posts/youtube/"
 +++
 
 ```rust
@@ -41,3 +41,21 @@ from concurrent.futures import ThreadPoolExecutor
 with ThreadPoolExecutor(max_workers=n_cores) as executor:
     executor.map(render, range(0, len(image_array)))
 ```
+
+```zig
+const std = @import("std");
+
+pub fn main() void {
+    const user = User{
+        .power = 9001,
+        .name = "Goku",
+    };
+
+    std.debug.print("{s}'s power is {d}\n", .{ user.name, user.power });
+}
+
+pub const User = struct {
+    power: u64,
+    name: []const u8,
+};
+```
diff --git a/content/posts/some_cool_stuff.md b/content/posts/some_cool_stuff.md
deleted file mode 100644
index 9de2829..0000000
--- a/content/posts/some_cool_stuff.md
+++ /dev/null
@@ -1,32 +0,0 @@
-+++
-title = "Some cool stuff"
-date = 2024-03-02T00:00:00+03:00
-draft = false
-
-[taxonomies]
-tags = ["test"]
-
-[extra]
-disable_comments = true
-toc = true
-+++
-
-Let's test manual anchor link declaration:
-
-# Heading 1 {#h1}
-
-## Heading 2
-
-Nice, let's test internal linking now: [my link](@/posts/typography.md#h1)
-
----
-
-Nice! Now let's test shortcodes with a youtube iframe embed video:
-
-{{ youtube(id="dCKeXuVHl1o") }}
-
----
-
-{{ youtube(id="dCKeXuVHl1o", autoplay=true) }}
-
-Cool! All these features should be plenty enough for now. I will add some others as we go.
diff --git a/content/posts/typography.md b/content/posts/typography.md
index 9a7d074..9164530 100644
--- a/content/posts/typography.md
+++ b/content/posts/typography.md
@@ -1,10 +1,10 @@
 +++
-title = "Typography"
-date = 2018-09-29T11:36:33+08:00
+title = "Test Typography For The Blog"
+date = 2025-01-26
 draft = false
 
 [taxonomies]
-tags = ["test", "original_post"]
+tags = ["test-formatting"]
 
 [extra]
 math = true
@@ -40,6 +40,10 @@ Inline styles to test:
 
 ###### Heading 6
 
+Let's test manual anchor link declaration:
+
+Nice, let's test internal linking now: [my link](@/posts/typography.md#h1)
+
 Cute Table:
 
 | Left-Aligned  | Center Aligned  | Right Aligned |
@@ -47,6 +51,7 @@ Cute Table:
 | col 3 is      | some wordy text |         $1600 |
 | col 2 is      |    centered     |           $12 |
 | zebra stripes |    are neat     |            $1 |
+|               |                 |               |
 
 Lists:
 
diff --git a/content/posts/youtube.md b/content/posts/youtube.md
new file mode 100644
index 0000000..2e52f39
--- /dev/null
+++ b/content/posts/youtube.md
@@ -0,0 +1,24 @@
++++
+title = "Test YouTube Video Embeds"
+date = 2025-01-28
+draft = false
+
+[taxonomies]
+tags = ["test-formatting"]
+
+[extra]
+disable_comments = true
+toc = false
++++
+
+Let's test shortcodes with a youtube iframe embed video:
+
+{{ youtube(id="dCKeXuVHl1o") }}
+
+---
+
+Now with `autoplay=true` :
+
+{{ youtube(id="dCKeXuVHl1o", autoplay=true) }}
+
+Cool ! All these features should be plenty enough for now. I will add others as we go.
diff --git a/content/posts/How I made this Blog with Zola.md b/content/posts/zola-blog.md
index 520ee1c..5fb797d 100644
--- a/content/posts/How I made this Blog with Zola.md
+++ b/content/posts/zola-blog.md
@@ -1,17 +1,17 @@
 +++
-title = "Hello Internet"
+title = "How I made this Blog with Zola"
 date = 2024-01-27
-draft = false
+draft = true
 
 [taxonomies]
-tags = ["original_post", "blog", "test"]
+tags = ["guide"]
 
 [extra]
 disable_comments = true
-toc = false
+toc = true
 +++
 
-Hello, World! This is my first post on my new blog. I'm excited to share my thoughts with you.
+Hello, Internet! This is my first post on my new blog. I'm excited to share my thoughts with you.
 
 First off, how did I make this? I used Zola - a static site generator written in Rust. It's fast, easy to use, and has lots of features.
 
diff --git a/static/Alphara.png b/static/Alphara.png
index ebb735c..7551312 100644
--- a/static/Alphara.png
+++ b/static/Alphara.png