Learn Spanish (Latin America): No se permiten bicicletas en el andén. - Bicycles are not permitted on the platform.

Because this sentence uses the reflexive passive (pasiva refleja). In this structure, the thing receiving the action (bicicletas) is actually the grammatical subject of the sentence. Since bicicletas is plural, the verb must match it in the plural form (se permiten).

Could I change the word order and say Bicicletas no se permiten en el andén?

You can, but it sounds much less natural. When using the reflexive passive to state rules, signs, or general facts, Spanish speakers almost always place the verb before the subject.

Why use se permiten instead of the literal translation son permitidas?

While no son permitidas bicicletas is grammatically correct (the true passive voice), everyday Spanish strongly prefers the se passive for general rules and announcements. The true passive often sounds overly formal or like a direct translation from English.

Why is there no article before bicicletas? Shouldn't it be las bicicletas?

When an unspecified plural noun is the subject of a reflexive passive sentence and comes directly after the verb, the article is usually dropped. Leaving it out emphasizes that bicycles in general are banned, rather than a specific group of bicycles.