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Lattice Paths for Persistent Diagrams [PDF]

Interpret Mach Intell Med Image Comput Topogr Data Anal Appl Med Data (2021), 2021
Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. In this paper, we first present a new lattice path representation for persistent diagrams.
Chung MK, Ombao H.
europepmc   +7 more sources

Lattice paths with catastrophes [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero.
Cyril Banderier, Michael Wallner
doaj   +6 more sources

A lattice on Dyck paths close to the Tamari Lattice

CoRR, 2023
International audienceWe introduce a new poset structure on Dyck paths where the covering relationis a particular case of the relation inducing the Tamari lattice.
Baril, Jean-Luc, Naima, Mehdi, Kirgizov, Sergey   +2 more
core   +6 more sources

Flip Paths Between Lattice Triangulations

Discrete Applied Mathematics, 2023
We present a $O(n^{\frac{3}{2}})$-time algorithm for the \emph{shortest (diagonal) flip path problem} for \emph{lattice} triangulations with $n$ points, improving over previous $O(n^2)$-time algorithms.
Sitharam, Meera, Sims, William
core   +4 more sources

Promotion of Lattice Paths by Riordan Arrays

Mathematics
This paper investigates the use of Riordan arrays in the enumeration and transformation of lattice paths through a combinatorial framework of promotion.
Aoife Hennessy, Kieran Murphy, Narciso Gonzaga, Paul Barry   +3 more
doaj   +2 more sources

Elliptic enumeration of nonintersecting lattice paths

Journal of Combinatorial Theory - Series A, 2007
. We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function.
Michael J Schlosser
exaly   +2 more sources

The number of lattice paths below a cyclically shifting boundary

Journal of Combinatorial Theory - Series A, 2009
We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result can be viewed as an extension of well-known enumerative formulae concerning lattice paths dominated by lines of integer ...
Rattan, Amarpreet, Irving, J., Rattan, A., A. Rattan, J. Irving   +4 more
exaly   +2 more sources

Coxeter Lattice Paths

, 2006
This talk concerns generating code for running computationally intensive numerical lattice QCD simulations on large parallel computers, using an approach based on the theory of Coxeter groups.
Ashby, Thomas J., Kennedy, Anthony D., Watt, Stephen M.   +2 more
core   +5 more sources

Jagged Partitions and Lattice Paths [PDF]

Annals of Combinatorics, 2009
A lattice-path description of $K$-restricted jagged partitions is presented. The corresponding lattice paths can have peaks only at even $x$ coordinate and the maximal value of the height cannot be larger than $K-1$. Its weight is twice that of the corresponding jagged partitions. The equivalence is demonstrated at the level of generating functions.
Jacob, P., Mathieu, P.
exaly   +3 more sources

Combinatorial Generation Algorithms for Directed Lattice Paths

Mathematics
Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified ...
Yuriy Shablya, Arsen Merinov, Dmitry Kruchinin   +2 more
doaj   +2 more sources