Alpha-Pangrams

A "pangrammic window" is a subsection of text which contains every letter of the alphabet at least once. This has been studied many times in the past, including how probable it is that a subsection of text of certain length will be pangrammic.

The notion of a pangram can be restricted further by requiring that not only do all of the letters of the alphabet need to appear in the text, but they must appear in alphabetical order. The following list of words in "alpha-pangrammic" (a term I think I am coining here):

ABColomb DEFer GHI JacK LiMN OPaQueR STUdy VieW foXY Zip

I don't know if the two ideas above have ever been merged into one topic of research. That is, I've never seen discussed the notion of an "alpha-pangrammic window".

I included a pangrammic window challenge in my PUZZLES FROM WONDERLAND Party whereby the teams had to search for the shortest basic pangrammic window (by hand!) in the text of Alice's Adventures in Wonderland. The shortest pangrammic window in that work of literature is of length 196 (spaces and punctuation are ignored) and occurs near the beginning of Chapter XII:

Alice looked at the jury-box, and saw that, in her haste, she had put the Lizard in head downwards, and the poor little thing was waving its tail about in a melancholy way, being quite unable to move. She soon got it out again, and put it right; 'not that it signifies much,' she said to herself; 'I should think it would be QUITE as much use in the trial one way up as the other.'

But what about alpha-pangrammacy? Obviously the window would likely be longer. But how much longer?

Well, with a quick PERL script, I believe I have found the answer:

'Oh, I BEG your pardon!' she exclaimed in a tone of great dismay, and began picking them up again as quickly as she could, for the accident of the goldfish kept running in her head, and she had a vague sort of idea that they must be collected at once and put back into the jury-box, or they would die.

'The trial cannot proceed,' said the King in a very grave voice, 'until all the jurymen are back in their proper places-- ALL,' he repeated with great emphasis, looking hard at Alice as he said do.

Alice looked at the jury-box, and saw that, in her haste, she had put the Lizard in head downwards, and the poor little thing was waving its tail about in a melancholy way, being quite unable to move. She soon got it out again, and put it right; 'not that it signifies much,' she said to herself; 'I should think it would be QUITE as much use in the trial one way up as the other.'

As soon as the jury had a little recovered from the shock of being upset, and their slates and pencils had been found and handed back to them, they set to work very diligently to write out a history of the accident, all except the Lizard, who seemed too much overcome to do anything but sit with its mouth open, gazing up into the roof of the court.

It would also be of interest to find a work where the shorst basic pangrammic window and the shortest alpha-pangrammic window were disjoint subsets of the text.

-- Eric

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