On Dilworth's decomposition theorem

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Fully Mechanized Proofs of Dilworths Theorem and Mirskys Theorem

We present two fully mechanized proofs of Dilworth’s and Mirsky’s theorems in the Coq proof assistant. Dilworth’s Theorem states that in any finite partially ordered set (poset), the size of a smallest chain cover and a largest antichain are the same. Mirsky’s Theorem is a dual of Dilworth’s Theorem. We formalize the proofs by Perles [2] (for Dilworth’s Theorem) and by Mirsky [5] (for the dual ...

متن کامل

On Seymour’s Decomposition Theorem

Let M be a class of matroids closed under minors and isomorphism. Let M be a 3-connected matroid in M with an N-minor and let N have an exact k-separation (A, B). If there exists a k-separation (X ,Y ) of M such that A ⊆ X and B ⊆ Y , we say the k-separation (A, B) of N is induced in M. In this paper we give new sufficient conditions to determine if an exact k-separation of N is induced inM.

متن کامل

On the Krohn-Rhodes Cascaded Decomposition Theorem

The Krohn-Rhodes theorem states that any deterministic automaton is a homomorphic image of a cascade of very simple automata which realize either resets or permutations. Moreover, if the automaton is counter-free, only reset automata are needed. In this paper we give a very constructive proof of a variant of this theorem due to Eilenberg.

متن کامل

The Cyclic Decomposition Theorem

Let V be a finite-dimensional F -vector space, and let T : V → V be a linear transformation. In this note we prove that V is a direct sum of cyclic T -invariant subspaces. More specifically, we prove that V is a direct sum of cyclic T -invariant subspaces whose annihilators are generated by powers of irreducible polynomials, and that the collection of these polynomials is uniquely determined. R...

متن کامل

The cyclic decomposition theorem

8 Matrices 16 8.1 Representation of vector spaces and linear transformations . . . . . . . . . . . . . . . 16 8.2 Similarity transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 8.3 Direct sums of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 8.4 The companion matrix of a polynomial . . . . . . . . . . . . . . . . . . . . . . . ....

متن کامل

ذخیره 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 Mathematics

سال: 1976

ISSN: 0012-365X

DOI: 10.1016/0012-365x(76)90032-7