Results 111 to 120 of about 20,234 (200)

Counting lattice paths in restricted planes

, 2000
The number of lattice paths of fixed length consisting of unit steps in the north, south, east or west directions in the plane {(x,y)∈R2|0⩽y⩽x} is shown.
Choi, Seulhee
core   +1 more source

Hamiltonian Intervals in the Lattice of Binary Paths

The Electronic Journal of Combinatorics
Let $\mathcal{P}_n$ be the set of all binary paths (i.e., lattice paths with upsteps $u = (1,1)$ and downsteps $d = (1,-1)$) of length $n$ endowed with the pointwise partial ordering (i.e., $P \le Q$ iff the lattice path $P$ lies weakly below $Q$) and let $G_n$ be its Hasse graph.
Ioannis Tasoulas, Kostas Manes, Aristidis Sapounakis   +2 more
openaire   +2 more sources

Heaps of pieces for lattice paths

We study heaps of pieces for lattice paths, which give a combinatorial visualization of lattice paths. We introduce two types of heaps: type $I$ and type $II$. A heap of type $I$ is characterized by peaks of a lattice path.
Shigechi, Keiichi
core  

Limits of areas under lattice paths

, 2009
We consider sequences of polynomials which count lattice paths by area. In some cases the reversed polynomials approach a formal power series as the length of the paths tend to infinity.
Drake, Brian
core   +1 more source

Lattice paths in regions with the catalan property

Journal of Combinatorial Theory, Series A, 1980
AbstractIf α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such that α0 = 0 < β0, αn < βn = n, and αi < i < βi for 1 ⩽ i ⩽ n − 1, let L denote the set of lattice points (p, q) such that 0 ⩽ p ⩽ n and αp ⩽ q ⩽ βp. We determine all such regions L with the property that the number of lattice paths from (0, 0) to (p, p) in
openaire   +1 more source

LatticeWorks: An open-source MATLAB toolbox for nonuniform, gradient and multi-morphology lattice generation, and analysis

Materials & Design
This study introduces an open-source MATLAB toolbox, LatticeWorks, that offers a versatile platform for generating and analysing lattice structures, facilitating the exploration of nonuniform, functionally graded designs.
Mahtab Vafaeefar, Kevin M. Moerman, Ted J. Vaughan   +2 more
doaj   +1 more source

Combinatorics of lattice paths

, 2014
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science.
Ncambalala, Thokozani Paxwell
core  

LATTICE PATHS RESTRICTED BY TWO PARALLEL HYPERPLANES

, 1985
In the present paper, a lattice path in the nonnegative orthant in the $ (k+1) $-dimensional integer lattice is considered. The generating functions are obtained for the numbers of lattice paths restricted by two parallel hyperplanes satisfying various ...
佐藤, 優子, Sato, Masako, Sado, Taishin   +2 more
core  

A lattice on Dyck paths close to the Tamari lattice

International audienceWe introduce a new poset structure on Dyck paths where the covering relation is a particular case of the relation inducing the Tamari lattice.
Baril, Jean-Luc, Naima, Mehdi, Kirgizov, Sergey   +2 more
core  

Osculating Lattice Paths and Alternating Sign Matrices

, 1997
Osculating lattice paths are sets of directed lattice paths which are not allowed to cross or have common edges, but are allowed common vertices. We derive a constant term formula for the number of such lattice paths. The formula is obtained by solving a
R. Brak
core