factoriallyadv.
/fakˈtɔːrɪəli/, U.S. /fækˈtɔriəli/ 1. Mathematics. As factors; by reference to factors; see factor n. 6a. Also: in a factorial way, as a factorial; see factorial n. 2.
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1842 London, Edinb., & Dublin Philos. Mag. 21 539 The work of computation reduces itself merely to calculating n · n + 1/ 2 elements, or the n(n + 1) cross-products out of which they are constituted, and combining them factorially after that law of the pyramid.
1874 Analyst 1 178 Each power of x or of a has for denominator its exponent taken factorially.
1899 Trans. Cambr. Philos. Soc. 17 12 The natural numbers do occur factorially in the denominators in this hypergeometric series.
1963 Michigan Technic Feb. 51/2 As the number of dimensions increases, this set of points increases factorially and hundreds of trials may be required.
2006 G. Freudenburg Algebraic Theory Locally Nilpotent Derivations i. 11 A subring A ⊂ B is factorially closed in B if and only if..the condition fg ∈ A implies f ∈ A and g ∈ A.
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1873 Sc. Law Reporter 10 356/1 The costs of a factor in gathering rents for Lovat, or recovering a special debt for Lovat..must be viewed in connection with the estate and the rent factorially managed; and must form a deduction from the sum recovered.
3. Photography. Using factorial development. See factorial adj.2 3. Now rare.
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1908 Amateur Photographer 21 July 57/2 For those who desire to work factorially, it may be well to say that the appearance is somewhat more rapid than with pyro-soda.
1920 Camera Craft Nov. 372/2 By developing factorially, the degree of development can be repeated or modified with equal accuracy.
1941 Newspaper World 8 Mar. 19/1 One would be able to capture all the subtleties of soft shades and incisive lines in a properly exposed and factorially-developed continuous tone negative.
4. Genetics. In terms of genetic factors or genes; by the agency of genes, genetically. See factor n. 8b. Now rare.
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the world > life > biology > biological processes > genetic activity > genetic components > [adverb] > factor
factorially1909
multifactorially1954
1909 W. Bateson Mendel's Princ. Heredity (new ed.) iv. 84 In all the cases yet studied the genetic properties of the pied types can be represented factorially by regarding the pattern or distribution of the colour as due to a distinct factor or to its absence.
1938 Bot. Rev. 4 299 This condition..could be expressed factorially as ff × FF.
1956 Adv. Genetics 8 91 A certain Gilia, Clarkia, or Nicotiana species..is differentiated genomically as well as factorially from its congeners.
5. Science. In terms of causative factors; spec. such that the individual effect of each of several factors may be experimentally investigated. See factor n. 7a.
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the world > relative properties > number > probability or statistics > [adverb] > other
factorially1935
stochastically1947
polymodally1959
pseudorandomly1963
1935 R. A. Fisher Design Exper. vi. 104 The second advantage..in a factorially arranged experiment, is that, in addition to measuring the effects of the four single ingredients..it measures also the 11 possible interactions between these ingredients.
1977 Ann. Internal Med. 86 555/1 The therapy thus involved two factors for evaluation: glucose (high or low) and mannitol (presence or absence) arranged factorially.
2009 T. A. Brown & O. Leyfer in D. J. Stein et al. Textbk. Anxiety Disorders (ed. 2) ii. 25/1 Although factorially distinct, the six disorder factors were highly intercorrelated.
This entry has been updated (OED Third Edition, September 2014; most recently modified version published online March 2022).
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adv.1842