In the last issue of Semagames, Josep M. Albaigès dealt with the interesting topic of group palindromes, emphasizing on its numerical point of view. The number of possibilities, as he proves, is huge. In particular, it made me think about the interest of searching words being group palindromes, that is semantic group palindromes, as I decided to call them to distinguish from the numerical ones. As it happens with the “pure” palindromes (in groups of 1), the semantic constraint clearly reduces the number of cases.

In the sequel, I would like to show the results of the search of this type of words using a home-made program. The search has been done on some spelling files of the editor Winedt. In particular, that of Catalan language contains 275.487 words, that of Spanish 247.049, and that of British English 151.791. I would say that these data bases of words are not complete at all and contain some words not accepted by the reference dictionaries. I would appreciate if some of you, readers, provided better data bases. At the same time, I left an executable version of my program in my web site http://www.ma1.upc.edu/~tonig/Jocssem8.exe.

To decide whether a word is a group palindrome or not, we require either an even number of reciprocally symmetric groups, for instance co-co, or an odd number of symmetric groups in such a way that the central group (namely, the “hinge group”) has only one character, as for instance in-t-e-r-p-r-e-t-in in Catalan, where “p” is central. If we would include those words in which the non-symmetric central group is allowed to have more than one character (as in r-emarca-r), then the number of cases would increase enormously (in Catalan, for instance, we would jump from 200 to 20.00 words). This is why we impose the constraint over the cardinality of the hinge group. It is worth to say that in some languages, like Catalan, there do not exist palindromes with an even number of paired symmetric groups, excluding obviously the “pure” palindromes (like tallat).

Beside each group palindrome we show a numerical sequence with the cardinal of the groups that compound the palindrome up to the word's equator, like co-lo-lo-co: 2,2, in-t-e-r-p-r-e-t-in: 2,1,1,1,1 or r-emarca-r: 1,6 (although this is not an accepted word). In particular, this list contains the pure palindromic words, represented by sequences with only 1's (tallat: 1,1,1).

Finally, just saying that the accents are hidden to facilitate the search.

Toni Guillamon ( mailto:antoni.guillamon@.upc.edu),

January 2002