Results 81 to 90 of about 56,264 (249)

Maximum Shattering

Journal of Combinatorial Designs, Volume 33, Issue 12, Page 456-470, December 2025.
ABSTRACT A family ℱ of subsets of [ n ] = { 1 , 2 , … , n } shatters a set A ⊆ [ n ] if for every A ′ ⊆ A, there is an F ∈ ℱ such that F ∩ A = A '. We develop a framework to analyze f ( n , k , d ), the maximum possible number of subsets of [ n ] of size d that can be shattered by a family of size k.
Noga Alon, Varun Sivashankar, Daniel G. Zhu   +2 more
wiley   +1 more source

Extremal Permanents of Laplacian Matrices of Unicyclic Graphs

Axioms
The extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable.
Tingzeng Wu, Xiuhong Wang, Xiangshuai Dong   +2 more
doaj   +1 more source

Mirror symmetry, Laurent inversion, and the classification of Q$\mathbb {Q}$‐Fano threefolds

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We describe recent progress in a program to understand the classification of three‐dimensional Fano varieties with Q$\mathbb {Q}$‐factorial terminal singularities using mirror symmetry. As part of this we give an improved and more conceptual understanding of Laurent inversion, a technique that sometimes allows one to construct a Fano variety X$
Tom Coates, Liana Heuberger, Alexander M. Kasprzyk   +2 more
wiley   +1 more source

Linking Bipartiteness and Inversion in Algebra via Graph-Theoretic Methods and Simulink

Complexity
Research for decades has concentrated on graphs of algebraic structures, which integrate algebra and combinatorics in an innovative way. The goal of this study is to characterize specific aspects of bipartite and inverse graphs that are associated with ...
Mohammad Mazyad Hazzazi, Muhammad Nadeem, Muhammad Kamran, Muhammad Arshad, M. I. Elashiry, Samuel Asefa Fufa   +5 more
doaj   +1 more source

Bayer noise quasisymmetric functions and some combinatorial algebraic structures [PDF]

Categories and General Algebraic Structures with Applications
Recently, quasisymmetric functions have been widely studied due to their big connection to enumerative combinatorics, combinatorial Hopf algebra and number theory.
Adnan Abdulwahid
doaj   +1 more source

7‐Location, weak systolicity, and isoperimetry

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract m$m$‐Location is a local combinatorial condition for flag simplicial complexes introduced by Osajda. Osajda showed that simply connected 8‐located locally 5‐large complexes are hyperbolic. We treat the nonpositive curvature case of 7‐located locally 5‐large complexes.
Nima Hoda, Ioana‐Claudia Lazăr
wiley   +1 more source

On Spectral Graph Determination

Mathematics
The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct ...
Igal Sason, Noam Krupnik, Suleiman Hamud, Abraham Berman   +3 more
doaj   +1 more source

Sorting probability for large Young diagrams

Discrete Analysis, 2021
Sorting probability for large Young diagrams, Discrete Analysis 2021:24, 57 pp. Let $P=(X,\leq_P)$ be a finite partially ordered set (or _poset_, for short). A _linear extension_ $L$ of $P$ is a total ordering $\leq_L$ on $X$ such that for every $x,y\in
Swee Hong Chan, Igor Pak, Greta Panova
doaj   +1 more source

Hopf algebras and the combinatorics of connected graphs in quantum field theory

, 2008
In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators.
Mestre, Angela, Oeckl, Robert
core   +1 more source

Real models for the framed little n$n$‐disks operads

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We study the action of the orthogonal group on the little n$n$‐disks operads. As an application we provide small models (over the reals) for the framed little n$n$‐disks operads. It follows in particular that the framed little n$n$‐disks operads are formal (over the reals) for n$n$ even and coformal for all n$n$.
Anton Khoroshkin, Thomas Willwacher
wiley   +1 more source