1 9 N ov 2 00 4 Lattices of lattice paths ∗
نویسندگان
چکیده
We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e., lattices of Dyck paths) and give a recursive construction for them. The last section is devoted to the presentation of a couple of open problems.
منابع مشابه
N ov 2 00 6 SPHERICAL DESIGNS AND ZETA FUNCTIONS OF LATTICES
We set up a connection between the theory of spherical designs and the question of minima of Epstein’s zeta function. More precisely, we prove that a Euclidean lattice, all layers of which hold a 4-design, achieves a local minimum of the Epstein’s zeta function, at least at any real s > n 2 . We deduce from this a new proof of Sarnak and Strömbergsson’s theorem asserting that the root lattices ...
متن کاملar X iv : m at h . C O / 0 41 16 10 v 1 2 7 N ov 2 00 4 CHAIN POLYNOMIALS OF DISTRIBUTIVE LATTICES ARE 75 %
It is shown that the numbers ci of chains of length i in the proper part L \ {0, 1} of a distributive lattice L of length l + 2 satisfy the inequalities c0 < . . . < c⌊l/2⌋ and c⌊3l/4⌋ > . . . > cl. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.
متن کامل2 7 N ov 2 00 1 Balanced d - lattices are complemented ∗
According to Chajda and Eigenthaler ([1]), a d-lattice is a bounded lattice L satisfying for all a, c ∈ L the implications (i) (a, 1) ∈ θ(0, c) → a ∨ c = 1; (ii) (a, 0) ∈ θ(1, c) → a ∧ c = 0; where θ(x, y) denotes the least congruence on L containing the pair (x, y). Every bounded distributive lattice is a d-lattice. The 5-element nonmodular lattice N 5 is a d-lattice. Theorem 1 A bounded latti...
متن کاملar X iv : h ep - l at / 9 91 10 02 v 1 2 N ov 1 99 9 1 The finite temperature QCD phase transition with domain wall fermions .
Results from the Columbia lattice group study of the QCD finite temperature phase transition with dynamical domain wall fermions on 16 × 4 lattices are presented. These results include an investigation of the U(1) axial symmetry breaking above but close to the transition, the use of zero temperature calculations that set the scale at the transition and preliminary measurements close to the tran...
متن کاملar X iv : n lin / 0 61 10 18 v 2 [ nl in . S I ] 1 1 N ov 2 00 6 GENERALIZED ISOTHERMIC LATTICES
We study multidimensional quadrilateral lattices satisfying simultaneously two inte-grable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Möbius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constrain...
متن کامل