-
mathematics known as
order theory, a
semimodular lattice, is a
lattice that
satisfies the
following condition:
Semimodular law a ∧ b <: a implies b <: a ∨ b...
-
geometric lattice is a
finite atomistic semimodular lattice, and a
matroid lattice is an
atomistic semimodular lattice without the ****umption of finiteness...
- and only if it is both
upper and
lower semimodular. For a
lattice of
finite length, the (upper)
semimodularity is
equivalent to the
condition that the...
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various generalizations of
modularity related to this
notion and to
semimodularity.
Modular lattices are
sometimes called Dedekind lattices after Richard...
-
Mathematical Society, p. 95, ISBN 9780821810255. *Stern,
Manfred (1999),
Semimodular Lattices.
Theory and Applications,
Encyclopedia of
Mathematics and its...
- 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...
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ground set E if and only if r is subcardinal, monotonic, and
locally semimodular, that is, for any X , Y ⊆ E {\displaystyle X,Y\subseteq E} and any e...
- p. 47.
Rutherford (1965),
Theorem 9.3 p. 25. Stern,
Manfred (1999),
Semimodular Lattices:
Theory and Applications,
Encyclopedia of
Mathematics and its...
-
Chorus Ensemble, the
following year. In 1976,
Roland introduced the
semimodular System 100 and the
modular System 700 synthesizers. In 1977, the company...
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elements form an antichain.
Every slim
lattice is planar. A
finite planar semimodular lattice is slim if and only if it
contains no cover-preserving diamond...
