Related papers: Lattice Path Enumeration
We give formulas for enumerating directed paths in the graded poset of semi-magic squares of size three. We give two applications of these formulas: an advanced example of Vandermonde convolution for finite graded posets, and a direct…
Similar to how standard Young tableaux represent paths in the Young lattice, Latin rectangles may be use to enumerate paths in the poset of semi-magic squares with entries zero or one. The symmetries associated to determinant preserve this…
We present general algorithms (fully implemented in Maple) for calculations of various quantities related to constrained directed walks for a general set of steps on the square lattice in two dimensions. As a special case, we rederive…
This is survey of some recent results connecting random matrices, non-colliding processes and queues.
This note presents a formula for the enumerative invariants of arbitrary genus in toric surfaces. The formula computes the number of curves of a given genus through a collection of generic points in the surface. The answer is given in terms…
A connected set in a graph is a non-empty set of vertices that induces a connected subgraph. In an infinite lattice, a connected set is often referred to as a lattice animal, whose enumeration up to isomorphism is a classical problem in…
We give a classification of Lattes maps on P^2.
We report an efficient methodology for enumerating the Hamiltonian walks in two and three dimensional lattices of large sizes, using the concept of centroids. This strategy, with the help of JAVA programming enables the exact computation of…
Fill each box in a Young diagram with the number of paths from the bottom of its column to the end of its row, using steps north and east. Then, any square sub-matrix of this array starting on the south-east boundary has determinant one. We…
This is a survey paper on Alegbraic Geometry over Lie Algebras
A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number…
Consider non-negative lattice paths ending at their maximum height, which will be called admissible paths. We show that the probability for a lattice path to be admissible is related to the Chebyshev polynomials of the first or second kind,…
I review the current status of hadronic structure computations on the lattice. I describe the basic lattice techniques and difficulties and present some of the latest lattice results; in particular recent results of the RBC group using…
Let M(n,k,r,s) be the number of ordered paths in the plane, with unit steps E or N, that intersect k times in which the first path ends at the point (r,n-r) and the second path ends at the point (s,n-s). Our main object of study in this…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
In this paper, we propose an algorithm to generate all possible graceful graphs (including trees) containing n vertices as lattice paths in a certain triangular lattice defined below. This lattice that corresponds to graphs containing n…
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.
We show how lattice paths and the reflection principle can be used to give easy proofs of unimodality results. In particular, we give a "one-line" combinatorial proof of the unimodality of the binomial coefficients. Other examples include…
A detour in a graph is a longest path. This thesis is mainly about connected, non-traceable graphs with the property that each vertex is the start (or end) vertex of a detour. There are also related results on claw-free, 2-connected,…
A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…