Undominated Alphabetic Sequences

UNDOMINATED ALPHABETIC SEQUENCES

by Ross Eckler
Word Ways, 1982

In past Word Ways articles, various authors have explored words which contain consecutive letters of the alphabet (1) in order and adjacent to each other, (2) in order but not necessarily adjacent, and (3) neither in order nor adjacent. The longer the consecutive letter sequence that can be found in a word, the more noteworthy it is; for example, oveRSTUffed is more interesting to the logologist than fiRST. I define an alphabetic sequence as undominated if a word can be found containing all the letters in that sequence, but no word can be found containing any longer sequence including all the letters of the original one. Thus, RSTU is an undominated sequence for words with letters adjacent and in order, for there are no words containing the pentagrams QRSTU or RSTUV, the hexagrams PQRSTU, QRSTUV or RSTUVW, and so on. On the other hand, RSTU is not an undominated sequence for words with letters neither in order nor adjacent; for VenTRiloQUiSt contains the more inclusive sequence QRSTUV.

In the table below, I identify all undominated sequences with respect to solid boldface words in the Merriam-Webster Pocket Dictionary, for the three conditions mentioned above. Accompanying each undominated sequence is the shortest word known:

Adjacent In Order	Not Adjacent In Order	Not Adjacent Not In Order

BC bobcat CD anecdote DEF deft FGH afghan GHI dunghill HIJ hijack KL ankle LMN calmness MNO somnolent NOP hope Q quit RSTU understudy UV mauve W we XY waxy	ABCDE ambuscade DEFG defog EFGHI prizefighting HIJK hijack JKL jackal KLMN kleptomania LMNO luminous MNOP monopoly OPQ opaque PQRS parquetries QRST quartermaster RSTU rostrum STUV destructive UVW purview WXY waxy	ABCDEF feedback CDEFGHI lightfaced GHIJK straightjacket IJKL jailbreak JKLM lumberjack KLMNOP kleptomania NOPQR propinquity PQRSTU perquisite QRSTUV ventriloquist RSTUVW liverwurst WXY waxy YZABC recognizably

Except for oveRSTUffed, mentioned earlier, I know of no other word with an alphabetic tetragram in the first list. In the second list, an ABCDE inferred form is given by ABsConDEr. The word lIGHtFACED appears to be the only one in the Pocket Dictionary with seven consecutive letters neither adjacent nor in order; I am indebted to Tom Pulliam for this discovery. In fact, there are very few other sixers in the Pocket Dictionary; Tom Pulliam found BACkFiElD, FIGurEHeaD, PRereQUiSiTe, PicTUReSQue, BArEFaCeD, tIGHtFistED, PhaNtOMLiKe, ForEsIGHteD, BioFEeDbACk, and FrIGHtEneD.

If one relaxes the requirements a bit, alternatives appear. If logical inferred forms are allowed, dunGHIll can be shortened to siGHIng in the first list, and straIGHtJacKet to HIJacKinG in the third. The hyphenated JacK-In-tHe-puLpit, with HIJKL, dominates JaILbreaK with IJKL. Both PROpiNQUiTieS and QUadRuPlicaTiONS, with NOPQRSTU, dominate NOPQR and PQRSTU in the third list. The latter words are both listed in singular form in the Pocket Dictionary, and the plural -s is specifically indicated in Webster's Third; nevertheless, one would feel more comfort-able with actual examples of usage, particularly for propinquities.

The analogous list of undominated squences with respect to words in Webster's Second or Third is given below:

Adjacent In Order	Not Adjacent In Order	Not Adjacent Not In Order

ABC dabchick CDE ecdemic DEF deft EFG trefgordd FGH afghan GHI sighing HIJ hijack IJK satlijk KL ankle LMN calmness MNOP limnophile OPQ popquiz QR miqra RSTU understudy UV mauve W we XYZ hyrdoxyzine YZAB analyzable	ABCDE ambuscade CDEF campodeiform DEFGH underfreight EFGHI prizefighting HIJK hijack JKL jacklight KLMNO Kilmarnock LMNOP limnophile NOPQ unopaque PQRS parquetries QRST quartermaster RSTUV interdestructive UVW purview WXY waxy XYZAB oxygenizable ZABC Mozambican	CDEFGHI lightfaced GHIJK straightjacket HIJKL kjeldahlize IJKLM jamlike KLMNOP kleptomania LMNOPQR quadripulmonary NOPQRSTU quadruplications PQRSTUV supraquantivalent RSTUVW liverwurst WXY waxy XYZABC benzoxycamphor YZABCDEF brazenfacedly

If one allows hyphenated words or dictionary phrases, the sequence ABCDEFGHI can be found: BrIGHt-FACED and BlACkFacED HIGhland (both noted by Dmitri Borgmann in Language on Vacation) and BlEACHInG FelD. For FGHIJKL, Darryl Francis notes the excellent HaLF-JoKInG, found in Webster's Second. For the record, all known Websterian words with alphabetic tetragrams are given below:

MNOP: gymnopaedia, gymnopedia, gymnopaedic, Gymnophilona, Gymnopaedes, limnophil, limnophile, limnophilous, Limnophilidae, limnophilid, Limnopithecus, limnoplankton, limnoplanktonic, somnopathy, somnopathist, Thamnophilus, Thamnophis, thamnophile, thamnophiline, Thamnophilinae

RSTU overstuff, overstuffed, overstudy, overstudied, overstud, overstudious, overstudiously, overstudiousness, understuff, understuffing, understumble, superstuff

There are several other Websterian words containing the sequence NOPQRSTU: preinquisition, prerequisition, proacquisition, superloquent, equipartitions, perquisition, prequestion and prequalifications. However, none of these match the hyphenated word in the Random House Unabridged Dictionary containing LMNOPQRSTU, found by Ralph Beaman: QUaSi-cOMPLemeNTaRy.

The study of undominated squences can be carried out for reversed alphabets as well. For Websterian words, the undominated list for letters adjacent and in order is given below:

YX asphyxiate
XW boxweed
WV howve
VUT kevutzah
UTS nuts
SR classroom
RQ torque
PONM tamponment
ML firmly
LKJ stolkjaerre
JIH jihad
HG churchgoing
GFE songfest
FED fed
EDC bedclothes
CBA bacbakiri
BAZY carbazylic