Minimum matrix representation of Sperner systems
نویسندگان
چکیده
منابع مشابه
Minimum matrix representation of closure operations
Let (I be a column of the fft x /I matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal in A but different in a. It is easy IO see that if Y,~,(A) denotes . the columns implied by A, than :/,,,(A) is a closure operation. We say that M represents this closure operation. s(:/ ) is the minimum number of the rows of the matrices representing a given closure ...
متن کاملOn Saturated k-Sperner Systems
Given a set X, a collection F ⊆ P(X) is said to be k-Sperner if it does not contain a chain of length k + 1 under set inclusion and it is saturated if it is maximal with respect to this property. Gerbner, Keszegh, Lemons, Palmer, Pálvölgyi and Patkós conjectured that, if |X| is sufficiently large with respect to k, then the minimum size of a saturated k-Sperner system F ⊆ P(X) is 2k−1. In this ...
متن کاملMatrix Representation of Spiking Neural P Systems
Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In this work, a discrete structure representation of SN P systems with extended rules and without delay is proposed. Specifically, matrices are used to represent SN P systems. In order to represent the computations of SN P systems...
متن کاملShattering-extremal set systems from Sperner families
We say that a set system F ⊆ 2 shatters a given set S ⊆ [n] if 2 = {F ∩ S : F ∈ F}. The Sauer-Shelah lemma states that in general, a set system F shatters at least |F| sets. Here we concentrate on the case of equality. A set system is called shattering-extremal if it shatters exactly |F| sets. A conjecture of Rónyai and the second author and of Litman and Moran states that if a family is shatte...
متن کاملSperner capacities
We determine the asymptotics of the largest family of qualitatively 2{independent k{ partitions of an n{set, for every k > 2. We generalize a Sperner-type theorem for 2{partite sets of KK orner and Simonyi to the k{partite case. Both results have the feature that the corresponding trivial information-theoretic upper bound is tight. The results follow from a more general Sperner capacity theorem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1998
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(96)00051-0