なし (無し) is used to express the absence of something, meaning "without" or "no/none." It attaches to nouns to indicate that something is lacking or not present.
When placed directly after a noun, なし states that something does not exist or is absent. This is common in concise or written expressions.
The particle で can follow なし to indicate performing an action without something. This is one of the most common spoken patterns.
The particle に can follow なし, often carrying a nuance of doing something without prior arrangement or permission.
なし can modify another noun using の, functioning like a な-adjective.