Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Derangement |
DerangementNoun1. A state of mental disturbance and disorientation. 2. The act of disturbing the mind or body; "his carelessness could have caused an ecological upset"; "she was unprepared for this sudden overthrow of their normal way of living". Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "derangement" was first used in popular English literature: sometime before 1776. (references) |
| Domain | Definition |
Math | A permutation of elements, where no element is in its original position. (references) |
Source: compiled by the editor from various references; see credits. | |
(From Wikipedia, the free Encyclopedia)
Derangements arise in a number of guises in combinatorial problems. For example, each solution to the rooks problem, where n rooks must be placed on an n x n chessboard such that no two rooks occupy the same row or column, can be considered as a derangment of n elements. Another version of the problem arises when we ask for the number of ways n letters, each addressed to a different person, can be placed in n pre-addressed envelopes so that no letter appears in the correctly addressed envelope.
One approach to counting the derangements of n elements is to use induction. First, note that if φn is any derangement of the natural numbers [1,n], then for some k in [1,n-1], φn(n) = k. Then if we let (k,n) be the permutation of [1,n] which swaps k and n, and we let φn-1 be the composition ((k,n) o φn); then φn-1(n) = n, and either:
As examples of these two cases, consider the following two derangements of 6 elements as we perform the above described swaps:
514623 -> (51432)6; and
315624 -> (31542)6 -> (3142)56
The above described correspondences are 1-to-1. The converse is also true; there are exactly (n-1) ways of converting any derangement of n-1 elements into a derangement of n elements, and (n-1) ways of converting any derangement of n-2 elements into a derangement of n elements. For example, if n = 6 and k = 4, we can perform the following conversions of derangements of length 5 and 4, respectively
51432 -> 514326 -> 514623; and
3142 -> 31542 -> 315426 -> 315624
Thus, if we write dn as the number of derangements of n letters, and we define d0 = 1, d1 = 0; then dn satisfies the recurrence:
Perhaps a more well-known method of counting derangements uses the inclusion-exclusion principle.
Derangements are an example of the wider field of constrained permutations. For example, the ménage problem asks if n married couples are seated boy-girl-boy-girl-... around a circular table, how many ways can they be seated so that no man is seated next to his wife?
More formally, given sets A and S, and some sets U and V of surjections A → S, we often wish to know the number of pairs of functions (f,g) such that f is in U and g is in V, and for all a in A, f(a) ≠ g(a); in other words, where for each f and g, there exists a derangement φ of S such that f(a) = φ(g(a)).
Generalizations
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Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Derangement."
Synonyms: DerangementSynonyms: mental unsoundness (n), overthrow (n), unbalance (n), upset (n). (additional references) |
| Context | Synonyms within Context (source: adapted from Roget's Thesaurus). |
Arrangement | Noun: derangement; Verb: disorder; evection, discomposure, disturbance; disorganization, deorganization; dislocation; perturbation, interruption; shuffling; Verb: inversion; corrugation; (fold); involvement. |
Disorder | Noun: disorder; derangement; irregularity; anomaly; (unconformity); anarchy, anarchism; want of method; untidiness; Adjective: disunion; discord. confusion; confusedness; Adjective: mishmash, mix; disarray, jumble, huddle, litter, lumber; cahotage; farrago; mess, mash, muddle, muss, hash, hodgepodge; hotch-potch, hotch-pot; imbroglio, chaos, omnium gatherum, medley; mere mixture; fortuitous concourse of atoms, disjecta membra, rudis indigestaque moles. |
Insanity | Noun: disordered reason, disordered intellect; diseased mind, unsound mind, abnormal mind; derangement, unsoundness; psychosis; neurosis; cognitive disorder; affective disorder. |
| Source: adapted from Roget's Thesaurus. | |
Crosswords: Derangement |
| English words defined with "derangement": Disordination ♦ Functional disease ♦ insane ♦ Mania a potu ♦ Planetary aberration ♦ Synchysis. (references) |
| Specialty definitions using "derangement": axonal degeneration ♦ Muscular Atrophy ♦ neuroses ♦ physical shock ♦ Rheumatic Diseases. (references) |
| Etymologies containing "derangement": Disordination. (references) |
| Domain | Title |
Books |
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Source: compiled by the editor from various references; see credits. | |
| Author | Quotation |
Samuel Taylor Coleridge | My case is a species of madness, only that it is a derangement of the Volition, and not of the intellectual faculties. |
Source: compiled by the editor from various references. | |
| Title | Author | Quote |
Les Miserables | Hugo, Victor | Whenever Marius came in and went out, he carefully replaced the bar of the grating in such a way that no derangement was visible |
Source: compiled by the editor from various references. | ||
| Subject | Topic | Quote |
Health | The empiric use of FFP to reverse hemostatic disorders should be confined to those patients in whom factor deficiencies are presumed to be the sole or principal derangement. (references) | |
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| "Derangement" is generally used as a noun (singular) -- approximately 100.00% of the time. "Derangement" is used about 18 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Noun (singular) | 100% | 18 | 82,615 |
Source: compiled by the editor from several corpora; see credits.
Expression using "derangement": mental derangement. Additional references. | |
| Source: compiled by the editor from various references; see credits. |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Expression | Frequency per Day |
derangement | 17 |
derangement internal knee | 7 |
derangement internal | 4 |
derangement grand | 3 |
derangement knee | 2 |
| Source: compiled by the editor from various references; see credits. | |
| Language | Translations for "derangement"; alternative meanings/domain in parentheses. | |
Albanian | çrregullim (bewilderment, clutter, confusion, disarrangement, disarray, dislocation, disorder, disorganization, distemper, disturbance, excess, foul up, hugger mugger, mess, misrule, mix, muddle, muss, turmoil, upset), çmendje (going mad, queer). (various references) | |
Arabic | تشويش (disarrangement, disarray, dislocation, disruption, disturbance, garble, perturbation). (various references) | |
Bulgarian | умопомрачение (insanity, madness), разбъркване (disarrangement, mixing). (various references) | |
Chinese | 精神"乱. (various references) | |
Czech | duševní vyšinutí, porucha (breakdown, bug, defect, disorder, failure, fault, lesion), choromyslnost. (various references) | |
Danish | diffusionsforstyrrelse (diffusion derangement), kuldioxidnarkose (CO2 narcosis, mental derangement, mental derangement caused by CO2), jeg-forstyrrelse (derangement of the ego), epileptisk absencetilstand (epileptic derangement). (various references) | |
Dutch | ik-stoornis (derangement of the ego). (various references) | |
Finnish | mielenvika (mental derangement). (various references) | |
French | dérèglement. (various references) | |
German | unordnung (clutter, confusion, disarray, disorder, disorderliness, huggermugger, mess, muddle, untidiness), Störung (disorder, disruption, disturbance, fault, hitch, hold up, interference, interruption, intrusion, jamming, malfunction, perturbation, trouble, upset, violation), geistesgestörtheit. (various references) | |
Greek | ξεχαρβάλωμα (disorganization), παραφροσύνη (dementi, frenzy, insaneness, insanity, lunacy, madness), διαταραχή (disorder). (various references) | |
Hungarian | zűrzavar (anarchism, babel, chaos, cock-up, commotion, disarray, disorder, hassle, hubbub, huddle, hugger-mugger, hurly-burly, melee, mess-up, mix, mix-up, pandemonium, panic, picnic, screw-up, shambles, skein, stew, tangled skein, upturn), működési zavar, elmezavar (brainstorm, deliria, delirium, insanity, psychosis), üzemzavar (breakdown, bug, malfunction, trouble). (various references) | |
Indonesian | penyakit jiwa (alienation), gangguan (bother, disruption, disturbance, harassment, hindrance, interruption, irritation, nuisance, vexation). (various references) | |
Italian | disturbo (ailment, bother, complaint, disorder, disturbance, fault, illness, inconvenience, noise, obstruction, trouble, upset), squilibrio (disequilibrium, imbalance, insanity), sconvolgimento. (various references) | |
Japanese Kanji | 錯乱 (confusion, distraction). (various references) | |
Japanese Katakana | さくら" (confusion, distraction). (various references) | |
Manx | shaghrynys keeaylley, mee-oardagh (disarray), baanrys (dementia, fanaticism, madness). (various references) | |
Pig Latin | erangementday.(various references) | |
Portuguese | desarranjo (breakdown, colorwash, colourwash, disarrangement, disorder, perturbation, tumble), transtorno (moil, nuisance, overturn, trouble), perturbação (blankness, confusion, disarrangement, discomposure, disquiet, disturbance, embarrassment, flurry, fret, fuddle, gall, interference, ruffle, trepidation, turbidity, turbulence, turmoil, unrest, upheaval), loucura (brain sickness, crack, distraction, folly, foolishness, freak-out, frenzy, insanity, lunacy, madness, mania), avaria (average, breakdown, damage, prang). (various references) | |
Romanian | deranjare (annoyance, dislocation, disturbance, interruption, invasion, troubling), deranjament (damage, defect, disorder), alienaţie mintalã. (various references) | |
Russian | сумасшествие (craziness, dementia, distraction, insaneity, insanity, madness), психическое расстройство, приведение в беспорядок. (various references) | |
Serbo-Croatian | rastrojstvo (anomie, chaos, shatter). (various references) | |
Spanish | trastorno mental (thinking disorder, thought disorder), perturbacion (fault, obstruction). (various references) | |
Swedish | störning (disruption, distraction, disturbance, interference, jamming, perturbation), sinnesrubbning (mental disorder), rubbning (dislocation, dislodging, displacement, disturbance, upset), oordning (chaos, commotion, confusion, disarrangement, disarray, disorder, disturbance, mess, tangle, upset). (various references) | |
Turkish | dengesizlik (alienation, disequilibrium, imbalance, instability, mental alienation, unbalance, uneven temper), delilik (bug, craziness, crotchet, distraction, extravagance, Folly, foolery, insanity, lunacy, madness, mania, mental derangement, vagary, wildness), geçimsizlik (dissension, incompatiblity, misunderstanding). (various references) | |
Ukrainian | розлад (concision, disarray, disunity, frustration, malady, quarrel), безладдя (bewilderment, chaos, clutter, confusion, disarrangement, disorder, hoity toity, huddle, hugger mugger, mess, misrule, mix, moil, pell mell, pellmell, puddle, racket, shambles, sozzle, topsy turvy, upset, welter), психічний розлад, плутанина (boggle, confusion, embroilment, hubbub, hurly burly, intricacy, involute, jumble, maze, mingle-mangle, mishmash, mix up, muddle, muss, patchwork, pell mell, pellmell, puddle, skein, snarl, snarl up, tangle, wooliness, woolliness). (various references) | |
Vietnamese | tình trạng loạn trí, sự quấy rầy sự loạn trí, sự l m lộn xộn sự quấy rối. (various references) | |
| Source: compiled by the editor from various translation references. | ||
Derivations | |
Words beginning with "derangement": derangements. (additional references) | |
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"Derangement" is suggested in spellcheckers for the following: erangement. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-d-e-e-e-g-m-n-n-r-t" | |
-1 letter: endearment. | |
-2 letters: agreement, garmented, generated, greatened, margented, nemertean. | |
-3 letters: emendate, emergent, endanger, engender, gendarme, generate, mannered, meterage, neatened, remanent, remanned, renegade, reteamed, teenaged, teenager. | |
-4 letters: amender, angered, demerge, derange, deterge, dragnet, emender, emerged, endgame, enraged, entered, etagere, garment, gatemen, germane, grandee, granted, grantee, greaten, greened, greeted, grenade, margent, meander, metered, negated, negater, reagent, reedman. | |
| Words containing the letters "a-d-e-e-e-g-m-n-n-r-t" | |
+1 letter: derangements, endangerment. | |
+2 letters: endangerments. | |
+5 letters: governmentalized. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Commercial | 5. Quotations: Familiar 6. Quotations: Fiction 7. Quotations: Non-fiction 8. Usage Frequency | 9. Expressions 10. Expressions: Internet 11. Translations: Modern 12. Derivations | 13. Anagrams 14. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
