Well 00-00 is a palindrome, but this is somewhat contrived, as is 10-01. 11-11 would be the smallest "real" example. AnswerParty on!
A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. This process is sometimes called the 196-algorithm, after the most famous number associated with the process. In base ten, no Lychrel numbers have been yet proved to exist, but many, including 196, are suspected on heuristic and statistical grounds. The name "Lychrel" was coined by Wade VanLandingham as a rough anagram of Cheryl, his girlfriend's first name.
The reverse-and-add process produces the sum of a number and the number formed by reversing the order of its digits. For example, 56 + 65 = 121. As another example, 125 + 521 = 646.
A phonetic palindrome is a portion of sound or phrase of speech which is identical or roughly identical when reversed.
Some phonetic palindromes must be mechanically reversed, involving the use of sound recording equipment or reverse tape effects. Another, more abstract type are words which are identical to the original when separated into their phonetic components (according to a system such as the International Phonetic Alphabet) and reversed.
Constrained writing is a literary technique in which the writer is bound by some condition that forbids certain things or imposes a pattern.
Constraints are very common in poetry, which often requires the writer to use a particular verse form.