can putting up a fence be claimed as a permanent improvement?

Improvements to your own home are not deductible.  But save your receipts, invoices etc for someday when you sell the home.

When you make a home improvement, such as replacing the roof or building a fence, you can't deduct the cost in the year you paid for it, as xmasbaby0 states. But you should keep track of those expenses, because they can be used to reduce your taxes in the year you sell your house.

A fence could be considered a permanent improvement.  Permanent structures like a fence, a sidewalk, and a  sewer are considered to be permanent and add to the value of the property.

It would be added to the cost basis of your property and it may reduce your taxable capital gains when you sell. 

You add the cost of capital improvements to your cost basis of your house.

Your cost basis is the amount you'll subtract from the sales price to determine the amount of your profit when you sell it.

Click here for additional information on Home Improvements and your taxes.

Just an FYI:
All the responses here assume the home is your primary or second home and not a rental. If it's a rental then let it be known, as that "WILL" change the answer(s) to your question.