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The Collaborative International Dictionary

Permutation \Per`mu*ta"tion\, n. [L. permutatio: cf. F. permutation. See Permute.]

  1. The act of permuting; exchange of the thing for another; mutual transference; interchange.

    The violent convulsions and permutations that have been made in property.

  2. (Math.)

    1. The arrangement of any determinate number of things, as units, objects, letters, etc., in all possible orders, one after the other; -- called also alternation. Cf. Combination, n., 4.

    2. Any one of such possible arrangements.

  3. (Law) Barter; exchange.

    Permutation lock, a lock in which the parts can be transposed or shifted, so as to require different arrangements of the tumblers on different occasions of unlocking.

Douglas Harper's Etymology Dictionary

mid-15c., from Old French alternacion, from Latin alternationem (nominative alternatio), noun of action from past participle stem of alternare (see alternate (v.)).


n. 1 The reciprocal succession of (normally two) things in time or place; the act of following and being followed by turns; alternate succession, performance, or occurrence; as, the alternation of day and night, cold and heat, summer and winter, hope and fear. 2 The response of the congregation speaking alternately with the minister. 3 (context linguistics English) ablaut. 4 (context logic English) The "''inclusive or''" truth function. 5 (context mathematics English) A sequence that alternates between positive and negative values. (Sometimes wrongly used to mean a permutation.) 6 (context computing English) A construct in a regular expression that can match any of several specified subexpressions.

  1. n. being regularly exchangeable

  2. successive change from one thing or state to another and back again

Alternation (linguistics)

In linguistics, an alternation is the phenomenon of a phoneme or morpheme exhibiting variation in its phonological realization. Each of the various realizations is called an alternant. The variation may be conditioned by the phonological, morphological, and/or syntactic environment in which the morpheme finds itself.

Alternations provide linguists with data that allow them to determine the allophones and allomorphs of a language's phonemes and morphemes and to develop analyses determining the distribution of those allophones and allomorphs.

Alternation (solitaire)

Alternation is a Patience game which is played using two decks of playing cards. Its tableau (or playing area) is similar to that of another solitaire game, Stonewall.

Alternation (geometry)

In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.

Coxeter labels an alternation by a prefixed by an h, standing for hemi or half. Because alternation reduce all polygon faces to half as many sides, it can only be applied for polytopes with all even-sided faces. An alternated square face becomes a digon, and being degenerate, is usually reduced to a single edge.

More generally any vertex-uniform polyhedron or tiling with a vertex configuration consisting of all even-numbered elements can be alternated. For example, the alternation a vertex figure with 2a.2b.2c is a.3.b.3.c.3 where the three is the number of elements in this vertex figure. A special case is square faces whose order divide in half into degenerate digons. So for example, the cube 4.4.4 is alternated as which is reduced to 3.3.3, being the tetrahedron, and all the 6 edges of the tetrahedra can also be seen as the degenerate faces of the original cube.


Alternation may refer to:

  • Alternation (card game)
  • Alternation (linguistics), a variation in the phonological form of a morpheme
  • Diathesis alternation
  • Alternation (complexity), a resource in computational complexity theory
  • R/N alternation, see Rhotacism
  • AlterNation, a show on NE1 FM
  • Alternation (geometry), a geometric operation for deriving polytopes from other polytopes.
  • Alternation (formal language theory), the set union of two sets of strings in formal language theory and pattern matching
  • A name for logical disjunction, the or function
Alternation (formal language theory)

In formal language theory and pattern matching, alternation is the union of two sets of strings or patterns. As a pattern, the alternation of a and b matches either a or b.

In formal language theory, alternation is commutative and associative. This is not in general true in pattern-matching languages.

In the SNOBOL language, regular expression syntax, and some other languages, alternation is a binary infix operator on patterns, notated "|".

Alternation (string expansion)
  1. redirect Bash (Unix shell)#Brace expansion

Usage examples of "alternation".

The specific treatment, which should not be omitted, consists in administering doses of ten drops of the tincture of the muriate of iron in alternation with teaspoonful doses of the Golden Medical Discovery, every three hours.

Conditions necessary for these movements--List of Genera and Families, which include sleeping plants--Description of the movements in the several Genera--Oxalis: leaflets folded at night--Averrhoa: rapid movements of the leaflets--Porlieria: leaflets close when plant kept very dry--Tropaeolum: leaves do not sleep unless well illuminated during day--Lupinus: various modes of sleeping--Melilotus: singular movements of terminal leaflet--Trifolium--Desmodium: rudimentary lateral leaflets, movements of, not developed on young plants, state of their pulvini--Cassia: complex movements of the leaflets--Bauhinia: leaves folded at night--Mimosa pudica: compounded movements of leaves, effect of darkness--Mimosa albida, reduced leaflets of--Schrankia: downward movement of the pinnae--Marsilea: the only cryptogam known to sleep--Concluding remarks and summary--Nyctitropism consists of modified circumnutation, regulated by the alternations of light and darkness--Shape of first true leaves.

Few favored an outright duumvirate of twins, but several groups called for joint rule by annual alternation, citing various actual and mythical precedents, as a peaceful resolution of the question.

Utopian philosopher, therefore, was whether this was an inevitable alternation, whether human progress was necessarily a series of developments, collapses, and fresh beginnings, after an interval of disorder, unrest, and often great unhappiness, or whether it was possible to maintain a secure, happy, and progressive State beside an unbroken flow of poietic activity.

It was their top story the next day, morphed in alternation with a shot of the Purist ringleaders, heads covered by police coats, marching to the paddy wagons.

By a sort of stichomythic alternation each for a time is supposed to carry on his speech regardless of the other, so that to follow either connectedly the alternate lines must be read in sequence.

It was from this antiphonal song, this alternation of versicle and respond, that the religious drama of the Middle Ages took its rise.

Now, in contrast to the Occidental thinker, who covets alternation because in his cold climate action is the means of enjoyment, the Hindu, in the languid East, where repose is the condition of enjoyment, conceives the highest blessedness to consist in exemption from every disturbance, in an unruffled unity excluding all changes.

The employment of an infusion of red clover blossoms, in small doses, is of undoubted value in modifying the irritation of the air-passages, and may be used to good advantage with, or in alternation with the Golden Medical Discovery.

Conscientious but morose, I went about my studies, strode dismally through the rectilinear suburban streets to the Kleinhammer-Weg, visited Gretchen Scheffler, who told me about Strength through Joy trips to the land of the midnight sun, while I went right on comparing Goethe with Rasputin or, when I had enough of the cyclic and endless alternation of dark and radiant, took refuge in historical studies.

Every one of us is subject to alternations of overvaluation and undervaluation of ourselves.

That the periodicity is determined by the daily alternations of light and darkness there can hardly be a doubt, as will hereafter be shown.

The island rocked steadily along through the alternations of sun and moon under an empty sky, the air about them still and hot, hotter and stiller the farther south they went.

In the second subclass the modification depends to a large extent on external agencies, such as the daily alternations of light and darkness, or light alone, temperature, or the attraction of gravity.

Each has its huge white Wady, striping the country in alternation with dark-brown divides, and trending coastwards in the usual network.