Are they limited to the Perception rules, or are there burrowing-specific rules that I can't find?
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Burrowing does not provide an exception from the general rule that the location of all creatures is known to all other creatures at any time.
Burrowing does make it easier to break Line of Sight (while not explicitly stated, I think it's hard to dispute that a creature is in a heavily obscured square while burrowing). This enables the burrower to make a stealth check at the end of his movement to become hidden.
You could use Dungeoneering, but it is covered by Perception.
From the Compendium:
Make a Perception check to notice clues, detect secret doors, *spot imminent dangers(, find traps, follow tracks, listen for sounds behind a closed door, or locate hidden objects
All of those emphasised points relate to noticing a burrowing creature.
Burrowing [movement mode] A monster with a burrowing speed can move through loose earth at the stated speed and move through solid stone at half speed. A monster can't shift or charge while burrowing. A monster can't be seen while it's burrowing, but is can be heard with a successful Perception* check (opposed by the monster's Stealth check). [DMG, pg280]
So firstly a burrowing monster need to roll a Stealth vs Passive Perception when it moves, to remain hidden. If it's Stealth is higher than your passive perception, then on your turn you can take a minor action to make a Perception to locate the monster.
Finding a Hidden Creature Make a Perception to find a hidden creature... Success: The target is no longer hidden. If the target cannot be seen for some reason, it still knows where the target is located. [Rules Compendium, pg150]
Just throwing this bit in here, but if your attacking a creature that is burrowed then you might be taking a -2 for partial concealment or -5 for total concealment depending on it moving through soft or solid earth.