The following should not cause any surprise.
Martin Luther King, Jr. Day is a United States federal holiday marking the birthday of Rev. Dr. Martin Luther King, Jr. It is observed on the third Monday of January each year, which is around the time of King's birthday, January 15. The floating holiday is similar to holidays set under the Uniform Monday Holiday Act, though the act predated the establishment of Martin Luther King, Jr. Day by fifteen years.
The sign pictured above has appeared taped to the San Luis Obispo City Library main entrance every January for the last four or five years, possibly longer. Since discovering it, I've made a point of presenting myself to this door the first Tuesday following the third Monday of every January. I suppose it's possible, being a library and specializing in filing and shelving, that not only the sign itself, but this exact piece of paper has persisted throughout the years.

If you're wondering, as I did, how a library run by local government can observe a national holiday the day after its official date, the explanation is rather simple. As explained to me one year by the reference librarian, they can't observe holidays on Monday because the library is closed. The library's normal business days are Tuesday through Saturday with short days on Thursday in acknowledgment of Farmers Market, a big tradition here, and Saturday. They are forced, therefore, to observe holidays such as Martin Luther King, Jr. Day on Tuesday, when they are open. Of course, they do so by closing.

I wanted to ask how they observe National Library Week but she was already helping the next person in line.

I was jolted from sleep by the sound of firecrackers and the shouts and shrieks of small children. I had dozed off with a book in my hands. It seemed impossible that I had slept so long. But, my watch said only 9:00. The neighbors just down the hill, an extroverted bunch, were celebrating an early New Years for the children. More shrieks. More laughter. More pops and clatter. They were watching the ball in Times Square, I imagine. Midnight, by comparison, seemed more like an armed invasion. It boomed and echoed up and down the hillside. Double New Year. One for the children, one for the adults. And now one for the rest of us. Happy New Year.