And in the other model it is just application of g and making the resulting word cyclically reduced.

Here each column contains four consecutive numbers cyclically arranged, four running in one direction and four in the other.The numbers in the 2nd, 5th, 3rd, and 8th columns of the square may be similarly grouped.…Cited from Amusements in Mathematics, by Henry Ernest Dudeney

To put a set in normal order, order it as an ascending scale in pitch-class space that spans less than an octave.Then permute it cyclically until its first and last notes are as close together as possible.…

A word is called cyclically reduced, if its first and last letter are not inverse to each other.Every word is conjugate to a cyclically reduced word, and a cyclically reduced conjugate of a cyclically reduced word is a cyclic permutation of the letters in the word.…

In other words, species life history characteristics fluctuate cyclically under the influence of surrounding species.These periodic shifts in life history properties produce observable changes in community composition.…

For any ordered group and any central element that generates a cofinal subgroup of, the quotient group is a cyclically ordered group.Moreover, every cyclically ordered group can be expressed as such a quotient group.…

Given a cyclically ordered group and an ordered group, the product is a cyclically ordered group.In particular, if is the circle group and is an ordered group, then any subgroup of is a cyclically ordered group.…

A group is locally cyclic if and only if its lattice of subgroups is a distributive lattice.A cyclically ordered group is a group together with a cyclic order preserved by the group structure.Every cyclic group can be given a structure as a cyclically ordered group, consistent with the ordering of the integers (or the integers modulo the order of the group).…

Labor mobility was not a key issue due to the widespread nature of job losses across geographies and industries.Cyclically sensitive industries such as manufacturing and construction had the most significant job losses.One study referenced in the CRS research indicated that long-term unemployment can convert cyclical to structural unemployment through loss of skills.…

Dropping the "total" requirement results in a partial cyclic order.A set with a cyclic order is called a cyclically ordered set or simply a cycle.Some familiar cycles are discrete, having only a finite number of elements: there are seven days of the week, four cardinal directions, twelve notes in the chromatic scale, and three plays in rock-paper-scissors.…

As befits the complex nature of many East African systems, Karimojong age sets are themselves grouped into generation sets consisting of five consecutive age sets.There are four such generation sets in all; each permanently named and recurring cyclically roughly every century.At a given time, two of the generation sets will be active: one junior and one senior.…

Given a cyclically ordered group and an ordered group, the product is a cyclically ordered group.In particular, if is the circle group and is an ordered group, then any subgroup of is a cyclically ordered group.…

Gravitational forces from the sun, moon, and planets, solar pressure acting on the antennas, satellite body and magnetic fields create rotational disturbances.Since the satellite moves around the earth's center in its orbit, the forces described above vary cyclically.This tends to set up nutation of the satellite which is damped using ADCS.…

Every element of the free group can be written uniquely as a reduced word in S.A word is cyclically reduced if and only if every cyclic permutation of the word is reduced.…

A certain subset of this cycle of cuts is the Dedekind completion of the original cycle.Starting from a cyclically ordered set, one may form a linear order by unrolling it along an infinite line.This captures the intuitive notion of keeping track of how many times one goes around the circle.…

Administratively, these inefficiencies contribute to long waiting lists, which in turn: deny services to others, worsen community perception, and create lost income for clinics.Cyclically, long waiting lists have shown some increased dropout effects, further exacerbating the problem.Predicting patients at risk of dropping treatment is a difficult task that is still being researched.…

Having completely discharged these chemical defences, it can take up to four months for the millipede to replenish their supplies.Breeding takes place cyclically in spring and summer.Male G. marginata are capable of producing a pheromone which attracts females, although this is only believed to be effective over short distances.…

The fluid may go through an external processing step, and then it is flowed back through the heat exchanger in the opposite direction for further processing.Usually the application will use this process cyclically or repetitively.…

Since there are possible linear orders, there are possible cyclic orders.An infinite set can also be ordered cyclically.…

In mathematics, cyclically reduced word is a concept of combinatorial group theory.