Crossword Genius

A hospitable type on the ground floor gets walked on by one greeting visitors to The House (7,3)

Ross

I believe the answer is:

welcome mat

I'm a little stuck... Click here to teach me more about this clue!

'a hospitable type' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Perhaps there's a link between them I don't understand?

'on the ground floor gets walked on by one greeting visitors to the house' is the wordplay.
I cannot really see how this works, but
'on' could be 'at' (I've seen this in other clues) and 'at' is located in the answer.
'one' could be 'o' (I've seen this in other clues) and 'o' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Irish Times.
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