An "inference" is a rational deduction which is made based upon premises assumed to be true. It is a logical conclusion that can be drawn by using observation—in this case, through the reading of a text.
We can make an inference about Diana Moon Glampers, the Handicapper General of the strange futuristic society presented in "Harrison Bergeron." Although every citizen within this story who is seen as more beautiful, more intelligent, more capable, etc. than the standard "average" is given handicaps to mute or dull their abilities, we can infer that this is not true for the Handicapper General herself. Diana Moon Glampers oversees, regulates, and enforces the use of handicaps; at the conclusion of the story, she shoots and kills Harrison Bergeron and the ballet dancer for removing their handicaps and threatens to do the same to the musicians.
Clearly Glampers must possess at least some superior talents in order to hold this governmental position; yet she does not seem encumbered by any handicaps which could threaten the effectiveness of her rule. This exposes a crack in the system which otherwise allegedly aims to equalize everyone. We can make this interference based upon her unchecked power, her possession of a weapon, and the physical and mental speed with which she shuts down Harrison's coup.
An inference that can be made about a character from Vonnegut's "Harrison Bergeron" is that derived from the actions of Harrison once he escapes; namely, that power is corruptive.
When Harrison escapes from prison, he comes to the television station, and feeling his superiority, he takes over the station, shouting,
"I am the Emperor! ...Do you hear? I am the Emperor! Everybody must do what I say at once!" He stamped his foot and the studio shook.
"Even as I stand here--" he bellowed, "crippled, hobbled, sickened--I am a greater ruler than any man who ever lived! Now watch me become what I can become!"
Clearly, having been unjustly imprisoned causes Harrison to revolt and seek redress. But, when he finds himself in control of the studio and throws off his handicaps, his sense of power becomes corruptive because he names himself emperor:
"I am the greater ruler than any man who ever lived! Now watch me become what I can become!"
Then, he declares that he will select his Empress, and challenges one of the women to dare to rise. A beautiful ballerina comes to him and they leap through the air "in an explosion of joy and grace" as they express their superiority.