Permutations assigned to slim rectangular lattices
نویسندگان
چکیده
منابع مشابه
Slim Semimodular Lattices. I. A Visual Approach
A finite lattice L is called slim if no three join-irreducible elements of L form an antichain. Slim lattices are planar. Slim semimodular lattices play the main role in [3], where lattice theory is applied to a purely group theoretical problem. After exploring some easy properties of slim lattices and slim semimodular lattices, we give two visual structure theorems for slim semimodular lattices.
متن کاملPolynomial Permutations on Finite Lattices Related to Cryptography
Motivated by cryptography, permutations induced by polynomial functions on finite lattices L = (L,∨,∧,∗ ) with an antitone involution ∗ are investigated. These permutations together with the operation of composition form a subgroup of the symmetric group on L. We describe the structure of this subgroup for different classes of lattices L and indicate possible applications by outlining a protoco...
متن کاملSlim Semimodular Lattices. II. A Description by Patchwork Systems
Rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in 2009. By a patch lattice we mean a rectangular lattice whose weak corners are coatoms. As a sort of gluings, we introduce the concept of a patchwork system. We prove that every glued sum indecomposable planar semimodular lattice is a patchwork of its maximal patch lattice intervals “sewn togeth...
متن کاملIntegrals over classical Groups, Random permutations, Toda and Toeplitz lattices
2 Two-Toda lattice and reductions (Hänkel and Toeplitz) 17 2.1 Two-Toda on Moment Matrices and Identities for τ -Functions 18 2.2 Reduction to Hänkel matrices: the standard Toda lattice and a Virasoro algebra of constraints . . . . . . . . . . . . . . . . . 26 2.3 Reduction to Toeplitz matrices: two-Toda Lattice and an SL(2,Z)algebra of constraints . . . . . . . . . . . . . . . . . . . . . . 29...
متن کاملIntegrable Lattices : Random Matrices and Random Permutations ∗ Pierre
These lectures present a survey of recent developments in the area of random matrices (finite and infinite) and random permutations. These probabilistic problems suggest matrix integrals (or Fredholm determinants), which arise very naturally as integrals over the tangent space to symmetric spaces, as integrals over groups and finally as integrals over symmetric spaces. An important part of thes...
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: Acta Scientiarum Mathematicarum
سال: 2016
ISSN: 0001-6969
DOI: 10.14232/actasm-015-271-y