How to track number of items sold on our partner site?

So we have a partner that sells products on their site.
We want to keep track of the number of items a user purchases coming from our site.

For example,
We refer a user to buy a certain product from our partner site. The user clicks on the link and goes to the product page. Instead of buying one, he decides to buy 5 of those items from our partner site.

How do we keep track of the number of items the user purchases?

I can't figure out how a referral code or pixel tracker can do all of this for us.

 

Ask your partner to have a copy of all the orders from their website.

Normally, all ecommerce software has this feature, like forward orders to these emails.

The free version of Interspire Shopping Cart has this.
http://www.iscexperts.com/viewtopic.php?f=2&t=11

 

If your eCommerce don't have any product tracking facilities [with tokens or referral code] that you have to consult a expert to setup your eCommerce with web analytics tools. You may aware about major analytics tools like: Google Analytics, Bing Analytics.

From that you can make track on your products.

 

These days such information is available for sharing with deals aggregators. Check with your partner if they publish it in their XML feed. Proving XML feed to deals aggregators will help your partners reach out to millions.