Results 61 to 70 of about 11,631 (230)
C-Finite Sequences and Riordan Arrays
MathematicsMany prominent combinatorial sequences, such as the Fibonacci, Lucas, Pell, Jacobsthal and Tribonacci sequences, are defined by homogeneous linear recurrence relations with constant coefficients.
Donatella Merlini
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Quantification and Determination of Compatible Bacterial Consortia
Microbial Biotechnology, Volume 18, Issue 9, September 2025.This study presents a mathematical model to identify compatible bacterial consortia by analysing antagonistic and coexistence relationships. Introducing the Bacterial Coexistence Index (BCI), it evaluates bacterial viability. The model identified 36,851 strain sets promoting plant growth, optimising bacterial consortium design for sustainable ...
Jair J. Pineda‐Pineda +4 more
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History of Catalan numbers [PDF]
, 2014 We give a brief history of Catalan numbers, from their first discovery in the 18th century to modern times. This note will appear as an appendix in Richard Stanley's forthcoming book on Catalan numbers.Comment: 10 ...
Pak, Igor
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Conformal Hypergraphs: Duality and Implications for the Upper Clique Transversal Problem
Journal of Graph Theory, Volume 109, Issue 4, Page 466-480, August 2025.ABSTRACT Given a hypergraph ℋ, the dual hypergraph of ℋ is the hypergraph of all minimal transversals of ℋ. The dual hypergraph is always Sperner, that is, no hyperedge contains another. A special case of Sperner hypergraphs are the conformal Sperner hypergraphs, which correspond to the families of maximal cliques of graphs.
Endre Boros +3 more
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Sequentially Constrained Hamilton Cycles in Random Graphs
Random Structures &Algorithms, Volume 67, Issue 1, August 2025.ABSTRACT We discuss the existence of Hamilton cycles in the random graph Gn,p$$ {G}_{n,p} $$ where there are restrictions caused by (i) coloring sequences, (ii) a subset of vertices must occur in a specific order, and (iii) there is a bound on the number of inversions in the associated permutation.
Alan Frieze, Wesley Pegden
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On the sub-permutations of pattern avoiding permutations
, 2014 There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees.
Disanto, Filippo, Wiehe, Thomas
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Canonical Labeling of Latin Squares in Average‐Case Polynomial Time
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT A Latin square of order n$$ n $$ is an n×n$$ n\times n $$ matrix in which each row and column contains each of n$$ n $$ symbols exactly once. For ε>0$$ \varepsilon >0 $$, we show that with high probability a uniformly random Latin square of order n$$ n $$ has no proper subsquare of order larger than n1/2log1/2+εn$$ {n}^{1/2}{\log}^{1/2 ...
Michael J. Gill +2 more
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Thom series of contact singularities [PDF]
, 2010 Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic ...
Fehér, L. M., Rimányi, R.
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ENUMERATIVE COMBINATORICS AND CODING THEORY
, 1994 The author develops a new method of investigation of combinatorial problems, introducing the value enumerator \(V_ f(T)= \sum_ p T^{f(p)}\in \mathbb{N}[T,T^{-1}]\) \((p\in \{1,-1\}^ n)\) for a certain polynomial \(f\) in \(n\) variables with non-negative integral coefficients. The coefficient of \(T^ v\) is the number of binary points \(p\) such that \(
openaire +3 more sources
Optimal Zero‐Free Regions for the Independence Polynomial of Bounded Degree Hypergraphs
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT In this paper, we investigate the distribution of zeros of the independence polynomial of hypergraphs of maximum degree Δ$$ \Delta $$. For graphs, the largest zero‐free disk around zero was described by Shearer as having radius λs(Δ)=(Δ−1)Δ−1/ΔΔ$$ {\lambda}_s\left(\Delta \right)={\left(\Delta -1\right)}^{\Delta -1}/{\Delta}^{\Delta ...
Ferenc Bencs, Pjotr Buys
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