Results 41 to 50 of about 11,854 (238)

A Covering pursuit game

Mathematika, Volume 72, Issue 1, January 2026.
Abstract In the “Covering” pursuit game on a graph, a robber and a set of cops play alternately, with the cops each moving to an adjacent vertex (or not moving) and the robber moving to a vertex at distance at most 2 from his current vertex. The aim of the cops is to ensure that, after every one of their turns, there is a cop at the same vertex as the ...
Benjamin Gillott
wiley   +1 more source

Enumeration of simple random walks and tridiagonal matrices

, 2002
We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the $n$-th power of a tridiagonal matrix and the enumeration of weighted ...
Bauer M, Flajolet P, G M Cicuta, Gessel I, Goldsheid I Y, Goulden I P, Jani M, Jonsson T, Klarner D A, Krattenthaler C, L Molinari, Lee D S, M Contedini, Mansour T, Merlini D, Mohanty G, Noh J D, Raykin M, Sachov V, Sinai Ya G, Sinai Ya G, Stanley R P, Stanley R P, Wigner E   +23 more
core   +1 more source

Fast Construction on a Restricted Budget

Random Structures &Algorithms, Volume 67, Issue 4, December 2025.
ABSTRACT We introduce a model of a controlled random graph process. In this model, the edges of the complete graph Kn$$ {K}_n $$ are ordered randomly and then revealed, one by one, to a player called Builder. He must decide, immediately and irrevocably, whether to purchase each observed edge.
Alan Frieze, Michael Krivelevich, Peleg Michaeli   +2 more
wiley   +1 more source

Globally nilpotent differential operators and the square Ising model

, 2008
We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and ...
Bostan, A., Boukraa, S., Hassani, S., Maillard, J. -M., Weil, J. -A., Zenine, N.   +5 more
core   +3 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   +1 more source

(Random) Trees of Intermediate Volume Growth

Random Structures &Algorithms, Volume 67, Issue 4, December 2025.
ABSTRACT For every function g:ℝ≥0→ℝ≥0$$ g:{\mathbb{R}}_{\ge 0}\to {\mathbb{R}}_{\ge 0} $$ that grows at least linearly and at most exponentially, if it is sufficiently well‐behaved, we can construct a tree T$$ T $$ of uniform volume growth g$$ g $$, or more precisely, C1·g(r/4)≤|BG(v,r)|≤C2·g(4r),for allr≥0andv∈V(T),$$ {C}_1\cdotp g\left(r/4\right)\le \
George Kontogeorgiou, Martin Winter
wiley   +1 more source

Transitive factorizations of permutations and geometry [PDF]

, 2014
We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves.
Goulden, I. P., Jackson, D. M.
core  

Extremal, enumerative and probabilistic results on ordered hypergraph matchings

Forum of Mathematics, Sigma
An ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders.
Michael Anastos, Zhihan Jin, Matthew Kwan, Benny Sudakov   +3 more
doaj   +1 more source

Chordal Graphs, Even‐Hole‐Free Graphs and Sparse Obstructions to Bounded Treewidth

Journal of Graph Theory, Volume 110, Issue 3, Page 351-365, November 2025.
ABSTRACT Even‐hole‐free graphs pose a central challenge in identifying hereditary classes of bounded treewidth. We investigate this matter by presenting and studying the following conjecture: for an integer t ≥ 4 and a graph H, every even‐hole‐free graph of large enough treewidth has an induced subgraph isomorphic to either K t or H, if (and only if) H
Sepehr Hajebi
wiley   +1 more source

Cyclic derangements [PDF]

, 2010
A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we generalize this problem
Assaf, Sami H.
core   +3 more sources