# Liquidity Providers

Liquidity providers supply liquidity to a pool for traders to swap against. In return for supplying liquidity, LPs receive swap fees from trades. The liquidity that is provided to a pool is represented by liquidity tokens. These tokens represent a proportional share of the liquidity pool and reservoir(s). The liquidity in a reservoir does not earn fees but can be reintegrated into the liquidity pool by LPs. This reintegration or balancing of a pool is done by adding single-sided liquidity. The protocol places constraints on this process to protect LPs further.

## Adding Liquidity

LPs can add liquidity to an existing pool in two different ways:

1. **Double-Sided:** Depositing liquidity for both assets of the token pair at a proportional rate.
2. **Single-Sided:** Depositing liquidity for the asset with less liquidity, further balancing out the pool.

Let *<mark style="color:blue;">`‘s’`</mark>* represent the number of liquidity tokens, and *<mark style="color:blue;">`‘z’`</mark>* represent the total number of tokens in the pool:

$$
s\_-minted/s\_-starting=z\_-deposited/z\_-starting
$$

{% hint style="info" %}
LPs will always be able to deposit an equivalent amount of <mark style="color:blue;">`Token X`</mark> and <mark style="color:blue;">`Y`</mark>. When one reservoir, i.e. <mark style="color:blue;">`Token X`</mark>, is partially filled, LPs can mint liquidity tokens by depositing <mark style="color:blue;">`Token Y`</mark> to balance the pool. &#x20;
{% endhint %}

## Removing Liquidity

There are two types of redemption:&#x20;

1. LPs can withdraw liquidity and redeem (burn liquidity tokens) for a proportional share of the pool and reservoir
2. LPs can withdraw from a single-asset reservoir up to the total number of tokens in the reservoir.

{% hint style="info" %}
Option #1 will always be available to LPs, resulting in an equivalent withdrawal of <mark style="color:blue;">`Token X`</mark> and <mark style="color:blue;">`Token Y`</mark>. If one reservoir is partially filled, i.e. <mark style="color:blue;">`Token X`</mark>, LPs can redeem liquidity tokens for just <mark style="color:blue;">`Token X`</mark>.&#x20;
{% endhint %}

{% hint style="warning" %}
If you deposit single-asset liquidity, this does not mean you can redeem for a single asset.
{% endhint %}

## Initialization of a Pool

The creation of a pool determines the initial price of an asset pair and its resulting swap ratio. The initializer receives liquidity tokens for creating the pool. A larger amount of liquidity deposited will result in more liquidity tokens for the initializer. Increased liquidity will also lead to less slippage and a more stable pool.