Selectors: A theory of formal languages, semimodular lattices, and branching and shelling processes
نویسندگان
چکیده
منابع مشابه
Semimodular Lattices Theory and Applications
Stern, Manfred. Semimodular lattices: theory and applications. / Manfred Stern. p. cm. – (Encyclopedia of mathematics and its applications ; v. 73) Includes bibliographical references and index.
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In a ranked lattice, we consider two maximal chains, or “flags” to be i-adjacent if they are equal except possibly on rank i . Thus, a finite rank lattice is a chamber system. If the lattice is semimodular, as noted in [9], there is a “Jordan-Hölder permutation” between any two flags. This permutation has the properties of an Sn-distance function on the chamber system of flags. Using these noti...
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In this paper we prove that if !.l' is a finite lattice. and r is an integral valued function on !.l' satisfying some very natural then there exists a finite geometric (that is.• semimodular and atomistic) lattice containing asa sublatticesuch that r !.l'restricted to Sf. Moreover. we show that if, for all intervals of. semimodular lattices of length at most r(e) are given. then can be chosen t...
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A lattice L is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element f ∈ L such that at most half of the elements x of L satisfy f ≤ x. Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let m denote...
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In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices ha...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1984
ISSN: 0001-8708
DOI: 10.1016/0001-8708(84)90042-2