In the regular growth and repair of bones, the tissues undergo, as Virchow remarks,[911] a whole series of permutations and substitutions.
So variable are the permutations of these tissues, in themselves so nearly allied, and yet in their external appearance so completely distinct.
The geographical names of places are signalled by four flags from ABCD to BFAU, while the permutations from CBDF to CZYX are used for an alphabetical spelling table.
Itacisms and permutationsof consonants are very frequent, and the text is of an unusual and interesting character.
This copy abounds as much as any with real variations from the common text, and with numberless errors of the pen, itacisms of vowels, and permutations of consonants.
Owing to the fact that the upper and lower arms are unequal in length, permutations will repeat by reflection, but not by reversal, for we cannot reverse.
We can do this in twenty-four different ways by forming all permutations of the letters.
Within the group differences of pattern depend upon the presence or absence of this or that factor, the variety of pattern being the result of the many possible permutations and {146} combinations of these colour factors.
But some factors may be common to two or more groups, in which case some of the permutations of the factors would be similar in the groups and would result in identical or nearly identical pattern.
But when we come to read these chapters, they contain little that is of value, and resolve themselves mostly into permutations of Aristotle's logical phraseology.
The arguments which Occam the Nominalist opposes to those of Duns Scotus the Realist, are marked with the stamp of the same system, and consist only in permutations and combinations of the same elementary conceptions.
It is clear that a large class of problems in permutations can be solved in a similar manner, viz.
To take the simplest possible example, consider the problem of finding the number of permutations of n different letters.
We have to find the number of permutations such that exactly m of the letters are in places they originally occupied.
He is not the seat of a process of living, except in the sense that he is subject to a series of permutations enforced upon him by circumstances external and alien to him.
However far-reaching and various the employment of the rent concept in economic theory has been, it has through all permutations remained, what it was to begin with, a rubric in the classification of incomes.
Apperception in the one case and discretion in the other cease to be the mere registration of a simple and personally uncolored sequence of permutations enforced by the factors of the external world.
In genuine Lancashire we have first the old-accustomed permutations of the vowels.
Every group of finite order N can therefore be represented in concrete form as a transitive group of permutations on N symbols.
If r is the number of different sets of conjugate operations in the group, then, when the group of N permutations is completely reduced, (i.
Those permutations which leave the product unaltered constitute a group of order n!
It is known as the symmetric group of degree n, the only rational functions of the symbols which are unaltered by all possible permutations being the symmetric functions.
It has been seen at the beginning of this section that every group of finite order N can be presented as a group of permutations (i.
It has been seen that every group of finite order can be represented as a group of permutations performed on a set of symbols whose number is equal to the order of the group.
A group of degree n, which is not contained in the alternating group, must necessarily have a self-conjugate subgroup of index 2, consisting of those of its permutations which belong to the alternating group.
Hence the set of permutations constitutes a group which is simply isomorphic with the given group.
Thus to the N lines of the tableau there corresponds a set of N permutations performed on the N symbols, which includes the identical permutation that leaves each unchanged.
In accordance with the general definitions already given, a permutation-group is called transitive or intransitive according as it does or does not containpermutations changing any one of the symbols into any other.
Moreover, if SpSq = Sr, then the result of carrying out in succession the permutations which correspond to the pth and qth lines gives the permutation which corresponds to the rth line.
Nothing would be presupposed, nothing foreseen, and each turn of the kaleidoscope would exhibit another of the infinitely various permutations of human relationship.
What sunrises and sunsets do we here witness, and what a multitude of permutations and combinations pass before us during the day, as we watch from hour to hour one of the loveliest landscapes of New England!
A new element or permutator multiplies by an increasing figure all the permutations it finds.
Permutations are readily illustrated with squares or cubes of different colours, with numbers, or letters.
Quintilian, however, seems to think that the first four words only, or chiefly, are meant: though the possiblepermutations of these are few and would hardly need to be written down.
The endless possibilities of these syllabic, verbal, and other permutations had evidently impressed the imagination of Dionysius: together with their climax in literature itself, and in all the great types of literature.
The plein air school is this century’s contribution; after that there can only be permutations and combinations of the old.
We are not equipped to deal with so much subtlety, so much variety, so many permutations and combinations.
And when you think that each new generation is the casual victim of the way a previous generation was conditioned, as well as the inheritor of the environment that resulted, the possible combinations and permutations are enormous.
To give the child an idea of the normal position of prepositions a series of permutations may be made leaving the preposition and its object in their normal positions.
As the teacher proceeds to make permutations in the different sentences she should remember (for Italian) that the normal position of the adverb is after the verb (in the compound tenses it comes between the auxiliary and the participle).
In other sentences also where the adverb is, so to speak, an adjective to an adjective and therefore really affects the object (noun), similar permutations may be made.
One of the first permutations is to remove the adverb from those sentences where it performs the function of an adjective to the verb, thereby causing one action to be changed into another.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "permutations" in a variety of sentences. We hope that you will now be able to make sentences using this word.
