Let be a finite projective plane of order q (not necessarily desarguesian). Maximal arcs of degree d ( 2 ≤ d ≤ q- 1) are (k,d)-arcs in, where k is maximal with respect to the parameter d, in other words, k = qd + d - q.
Equivalently, one can define maximal arcs of degree d in as non-empty sets of points K such that every line intersects the set either in 0 or d points.
Some authors permit the degree of a maximal arc to be 1, q or even q+ 1. Letting K be a maximal (k, d)-arc in a projective plane of order q, if
- d = 1, K is a point of the plane,
- d = q, K is the complement of a line (an affine plane of order q), and
- d = q + 1, K is the entire projective plane.
All of these cases are considered to be trivial examples of maximal arcs, existing in any type of projective plane for any value of q. When 2 ≤ d ≤ q- 1, the maximal arc is called non-trivial, and the definition given above and the properties listed below all refer to non-trivial maximal arcs.
Read more about this topic: Maximal Arc
Other articles related to "definition, definitions":
... In medical dictionaries, definitions should to the greatest extent possible be simple and easy to understand, preferably even by the general public useful clinically or in related areas where ...
... the Brundtland Report, which included what is now one of the most widely recognised definitions "Sustainable development is development that meets the needs of the present without compromising the ability of future ... It offers an integrated vision and definition of strong sustainability ... It generates a more nuanced definition of sustainable development “the need to ensure a better quality of life for all, now and into the future, in a just and ...
... These three definitions may be described as the ethno-linguistic definition, the religious-cultural definition, and the patrilineal definition, respectively ...
... plants that resist human digestive enzymes, a definition that includes lignin and polysaccharides ... The definition was later changed to also include resistant starches, along with inulin and other oligosaccharides ... Official definition of dietary fiber differs a little among different institutions Organization (reference) Definition Institute of Medicine Dietary ...
... ESPN launched its 720p high-definition simulcast, originally branded as ESPNHD, on March 20, 2001 ... Live studio shows, along with most live events on ESPN, use high definition ... Footage from non-HD sources is presented in a standard definition, 43 format with stylized pillarboxes ...
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (17721834)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on life (based on wording in the First Edition, 1935)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)