# ALPHABETICAL PATTERNS

by Ross Eckler
Word Ways, 1993

Readers of Word Ways should be familiar with the concept of word patterns, exemplified by Jack Levine's three-volume rearrangement of Webster's Second and Third Editions into groups of words having the same pattern, such as EXCESS and BAMBOO. (Word patterns have even been discussed in large-circulation magazines; see physicist Sheldon Glashow's "The Game of Bop" in the Sep/Oct 1992 issue of Quantum.) It is the object of this article to show how the concept of alphabetic patterns can be similarly codified. The alphabetic pattern of a word is ascertained by writing the letters of the alphabet in a row on a slip of paper (in circular fashion, with Z followed by A), and sliding this strip back and forth underneath the word to identify letter-matches (crashes) with the letters of the word. For example, the letters of the word WRETCH match with four different alphabet-shifts, denoted by capital letters in the four alphabets below:

W R E T C H

W-alphabet . . u v W x y z a b c d . .

Q-alphabet . . o p q R s T u v w x . .

C-alphabet . . a b c d E f g H I j . .

Y-alphabet . . w x y z a b C d e f . .

The crashing alphabets are, for convenience, identified by the letter corresponding to the first letter in the word. If a letter matches the A-alphabet, it is said to be invariant.

One can characterize the alphabetic pattern of a word by the identifiers of the crashing alphabets; thus WRETCH has the alphabetic pattern WQCQYC, with two alphabets (W and Y) crashing once and two more (Q and C) crashing twice. Using this equivalence, one can classify all words in the dictionary by their alphabetic patterns, grouping together those (such as WQCQYC and PNDNXD) whose alphabetic patterns are equivalent. For brevity, each group is identified by its first pattern, alphabetically speaking (ABCBDC). In turn, groups can be assembled into supergroups which are identified by the number of singly-, doubly-, etc., crashing alphabets (WRETCH, for example, has two single-crashes and two double-crashes, as does LANCES, with the different alphabetic pattern LZLZAN). Both are in supergroup 2211.

These concepts can be illustrated by classifying the four-letter boldface words in the Merriam-Webster Pocket Dictionary according to their alphabetical patterns:

Supergroup 1111

Pattern ABCD 1538 (adze aeon aero aery afar ...)

Supergroup 211

Pattern AABC 68 (abbe abet able ably abut ...)
Pattern ABAC 70 (arch body chew clew crew ...)
Pattern ABCA 63 (acid amid arid avid auld ...)
Pattern ABBC 46 (alms anon baby chic chid ...)
Pattern ABCB 48 (ache acme acne acre ammo ...)
Pattern ABCC 97 (aide Arab atop balm bast ...)

Supergroup 31

Pattern AAAB 6 (deft defy nope stub stud stun)
Pattern ABAA 5 (bade bide bode chef clef)
Pattern AABA 2 (abed hick)
Pattern ABBB 1 (erst)

Supergroup 22

Pattern AABB 5 (hide high node stab stop)
Pattern ABAB 2 (grit spur)
Pattern ABBA 3 (babe shiv whiz)

Certain aspects of alphabetic patterns have been touched on in earlier Word Ways: the subject was introduced in a Query in May 1972. Invariant letters ending words (A, oB, saC, etc.) were explored by Darryl Francis in May 1971. Ed Wolpow listed words having four crashes with a particular alphabet in February 1979. The words iNOPeRaTiVe and coOPeRaTiVelY both have six crashes with a single alphabet. Shiftwords (such as JOLLY to CHEER, or OHM to PIN) always have the same alphabetic pattern.

Alphabetic patterns are analogous to the word patterns alluded to at the beginning of this article; in fact, any question about one can be rephrased as a question about the other. The key is to visualize the alphabetic pattern as a "word" in its own right. Thus, the search for the longest word in which each letter has its own unique alphabetic shift corresponds to the search for the longest isogram (word with no letter repeated). For the former, Leonard Gordon found the 18-letter word QUANTIFICATIONALLY in Webster's Third, which corresponds to DERMATOGLYPHICS. Similarly, the search for the word with the most letters matching a single shift-alphabet, the word iNOPeRaTiVe above, translates to the search for the word with the most repetitions of a single letter, hUmUhUmUnUkUnUkUapUaa. Leonard Gordon discovered HUMISTRATOUS is the longest-known word with each shift-alphabet appearing twice (pattern ABCDEEFBFCDA), which corresponds to the pair isogram SCINTILLESCENT. Words such as undeRSTUdy or liMNO-Phile have four consecutive letters in the same shift-alphabet, corresponding to Websterian words such as headmistreSSShip or waLLLess having three consecutive identical letters. No doubt Word Ways readers can discover other analogies.

Chris Cole has kindly supplied the author with a list of boldface uncapitalized unhyphenated words with six letters matching a single shift-alphabet. All can be found in one or more of three sources: the Second and Third Editions of the Merriam-Webster Unabridged, and the Random House Unabridged. By far the commonest match is OPRTVY, illustrated by OPeRaTiVelY and its derivatives (add prefixes co-, unco-, pre-, post- or intra-). OPeRaTiVitY offers another variant. NOPRTV is found in iNOPeRaTiVe, iNOPeRaTiVeness and noNOPeRaTiVe. NPRTUY appears in noNsPiRiTUallY and uNsPiRiTUallY. Other matches are illustrated by DauGHterLiNesseS, DEFinItiveNesseS, gyMNOPlaST, nEiGHborLiNesseS, unDEFendabLeNesseS, baLaNOPlaSTy and NOnfeSTiVelY.

Here is the corresponding list of words with five letters matching the A-alphabet: ABuDEFduf, AgammaGlobuLiNemiaS, ArChEncephaLoN, ArChEtypIcaL(ly), syngEnesIotraNsPlanTation, ABaDEnGo, AntiantHropoMorPhiSm, ApoDEictIcaL(ly), ArChErsHIp, nonDEFeasibLeNess, nonDEFensibLeNess, nonDEFinIteLy and nonDEFinItiveNess.