Definitions for antimatroid
an·ti·ma·troid

WiktionaryRate this definition:0.0 / 0 votes

1. antimatroidnoun

   a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included

WikipediaRate this definition:0.0 / 0 votes

1. Antimatroid

   In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts.The axioms defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead by an anti-exchange axiom, from which their name derives. Antimatroids can be viewed as a special case of greedoids and of semimodular lattices, and as a generalization of partial orders and of distributive lattices. Antimatroids are equivalent, by complementation, to convex geometries, a combinatorial abstraction of convex sets in geometry. Antimatroids have been applied to model precedence constraints in scheduling problems, potential event sequences in simulations, task planning in artificial intelligence, and the states of knowledge of human learners.

WikidataRate this definition:0.0 / 0 votes

1. Antimatroid

   In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. Dilworth was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts; see Korte et al. for a comprehensive survey of antimatroid theory with many additional references. The axioms defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead by an anti-exchange axiom, from which their name derives. Antimatroids can be viewed as a special case of greedoids and of semimodular lattices, and as a generalization of partial orders and of distributive lattices. Antimatroids are equivalent, by complementation, to convex geometries, a combinatorial abstraction of convex sets in geometry.

How to pronounce antimatroid?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say antimatroid in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of antimatroid in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of antimatroid in Pythagorean Numerology is: 7

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Antimatroid
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Antimatroid
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=antimatroid