Results 61 to 70 of about 74,505 (227)
Percolation on High‐Dimensional Product Graphs
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT We consider percolation on high‐dimensional product graphs, where the base graphs are regular and of bounded order. In the subcritical regime, we show that typically the largest component is of order logarithmic in the number of vertices. In the supercritical regime, our main result recovers the sharp asymptotic of the order of the largest ...
Sahar Diskin +3 more
wiley +1 more source
On some enumerative aspects of generalized associahedra [PDF]
arXiv, 2005 We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky to a finite root system and (b) the lattice of noncrossing partitions associated to the corresponding finite real reflection group.
arxiv
Typical Structure of Hereditary Graph Families. I. Apex‐free Families
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT A family of graphs ℱ$$ \mathcal{F} $$ is hereditary if ℱ$$ \mathcal{F} $$ is closed under isomorphism and taking induced subgraphs. The speed of ℱ$$ \mathcal{F} $$ is the sequence {|ℱn|}n∈ℕ$$ {\left\{|{\mathcal{F}}^n|\right\}}_{n\in \mathbb{N}} $$, where ℱn$$ {\mathcal{F}}^n $$ denotes the set of graphs in ℱ$$ \mathcal{F} $$ with the vertex ...
Sergey Norin, Yelena Yuditsky
wiley +1 more source
On the Edge‐Density of the Brownian Co‐Graphon and Common Ancestors of Pairs in the CRT
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT Bassino et al. have shown that uniform random co‐graphs (graphs without induced P4$$ {P}_4 $$) of size n$$ n $$ converge to a certain non‐deterministic graphon. The edge density of this graphon is a random variable Λ∈[0,1]$$ \boldsymbol{\Lambda} \in \left[0,1\right] $$ whose first moments have been computed by these authors.
Guillaume Chapuy
wiley +1 more source
A systematic literature review on the mathematical underpinning of model‐based systems engineering
Systems Engineering, Volume 28, Issue 1, Page 134-153, January 2025.Abstract The International Council on Systems Engineering (INCOSE) has initiated a Future of Systems Engineering (FuSE) program that includes a stream for advancing the theoretical foundations of the discipline of Systems Engineering (SE). A near‐term goal of FuSE is to assess the adequacy of current theoretical foundations of SE.
Paul Wach +5 more
wiley +1 more source
The Poincaré‐extended ab$\mathbf {a}\mathbf {b}$‐index
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Motivated by a conjecture concerning Igusa local zeta functions for intersection posets of hyperplane arrangements, we introduce and study the Poincaré‐extended ab$\mathbf {a}\mathbf {b}$‐index, which generalizes both the ab$\mathbf {a}\mathbf {b}$‐index and the Poincaré polynomial.
Galen Dorpalen‐Barry +2 more
wiley +1 more source
How Joe Gillis Discovered Combinatorial Special Function Theory [PDF]
Math. Intell. 17(2), 65-66, 1994 How Enumerative Combinatorics met Special Functions, thanks to Joe ...
arxiv
arXiv, 2014 This is a survey on permutation classes for the upcoming book Handbook of Enumerative Combinatorics.
arxiv
Three Ways to Count Walks in a Digraph [PDF]
arXiv, 2016 We approach the problem of counting the number of walks in a digraph from three different perspectives: enumerative combinatorics, linear algebra, and symbolic dynamics.
arxiv
New directions in enumerative chess problems [PDF]
Electronic Journal of Combinatorics 11(2) (2004-2005) [Stanley-60
Festschrift], Article #4, 2005 Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played. In an enumerative chess problem, the set of moves in the solution is (usually) unique but the order is not, and the task is to count the feasible permutations via an isomorphic ...
arxiv