Boolean degree 1 functions on some classical association schemes

DOI10.1016/j.jcta.2018.11.006zbMath1401.05317arXiv1801.06034OpenAlexW2963245721WikidataQ128991460 ScholiaQ128991460MaRDI QIDQ1633376

Yuval Filmus, Ferdinand Ihringer

Publication date: 19 December 2018

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.06034

zbMATH Keywords

completely regular codeGrassmann graphCameron-Liebler line classBoolean analysisassocation schemeBoolean degree 1 function

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30)

Related Items (25)

Log-Sobolev inequality for the multislice, with applications ⋮ Completely regular codes in Johnson and Grassmann graphs with small covering radii ⋮ Remarks on the Erdős matching conjecture for vector spaces ⋮ A modular equality for Cameron-Liebler line classes in projective and affine spaces of odd dimension ⋮ On completely regular codes with minimum eigenvalue in geometric graphs ⋮ Cameron–Liebler sets for maximal totally isotropic flats in classical affine spaces ⋮ Degree 2 Boolean functions on Grassmann graphs ⋮ Boolean functions on $S_n$ which are nearly linear ⋮ Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry ⋮ Junta threshold for low degree Boolean functions on the slice ⋮ High dimensional Hoffman bound and applications in extremal combinatorics ⋮ Unnamed Item ⋮ The chromatic number of the \(q\)-Kneser graph for large \(q\) ⋮ Cameron-Liebler \(k\)-sets in \(\text{AG}(n,q)\) ⋮ Cameron-Liebler sets of \(k\)-spaces in \(\mathrm{PG}(n,q)\) ⋮ Unnamed Item ⋮ Equivalent definitions for (degree one) Cameron-Liebler classes of generators in finite classical polar spaces ⋮ Cameron-Liebler line classes with parameter \(x = \frac{ ( q + 1 )^2}{ 3} \) ⋮ Cameron-Liebler sets in bilinear forms graphs ⋮ Cameron-Liebler line classes of \(\mathrm{PG}(3,q\)) admitting \(\mathrm{PGL}(2,q\)) ⋮ FKN theorem for the multislice, with applications ⋮ Perfect colorings of regular graphs ⋮ Boolean constant degree functions on the slice are juntas ⋮ Correction to: ``Cameron-Liebler sets of \(k\)-spaces in \(\mathrm{PG}(n,q)\) ⋮ Cameron-Liebler \(k\)-sets in subspaces and non-existence conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new family of tight sets in \(\mathcal Q^+(5,q)\)
• An Erdős-Ko-Rado theorem for finite 2-transitive groups
• An improved bound on the existence of Cameron-Liebler line classes
• Cameron-Liebler line classes in \(PG(n,4)\)
• A modular equality for Cameron-Liebler line classes
• A quasi-stability result for dictatorships in \(S_n\)
• Testing juntas
• Intriguing sets of vertices of regular graphs
• Cameron-Liebler line classes in PG(3,q)
• The Cameron-Liebler problem for sets
• Buildings of spherical type and finite BN-pairs
• Bilinear forms over a finite field, with applications to coding theory
• Subsets of association schemes corresponding to eigenvectors of the Bose-Mesner algebra
• The construction of Cameron-Liebler line classes in \(PG(3,q)\)
• Completely regular designs of strength one
• Width and dual width of subsets in polynomial association schemes
• Hermitian rank distance codes
• Derivation of Cameron-Liebler line classes
• Graph products, Fourier analysis and spectral techniques
• The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters
• Tactical decompositions and orbits of projective groups
• Boolean functions whose Fourier transform is concentrated on the first two levels.
• The eigenspaces of the Bose-Mesner algebras of the association schemes corresponding to projective spaces and polar spaces
• Cameron-Liebler line classes with parameter \(x = \frac{q^2 - 1}{2}\)
• Tight sets and \(m\)-ovoids of finite polar spaces
• A gap result for Cameron-Liebler \(k\)-classes
• Cameron-Liebler line classes in \(\mathrm{PG}(3,4)\)
• An orthogonal basis for functions over a slice of the Boolean hypercube
• Geometry of symmetric matrices over any field with characteristic other than two
• Antidesigns and regularity of partial spreads in dual polar graphs
• Friedgut--Kalai--Naor theorem for slices of the Boolean cube
• Erdős–Ko–Rado Theorems: Algebraic Approaches
• Some q-Krawtchouk Polynomials on Chevalley Groups
• Cameron‐Liebler line classes in PG(3, 5)
• LOW-DEGREE BOOLEAN FUNCTIONS ON , WITH AN APPLICATION TO ISOPERIMETRY
• On independent sets, 2-to-2 games, and Grassmann graphs
• Analysis of Boolean Functions
• A stability result for balanced dictatorships in S_n
• Invariance principle on the slice
• Harmonicity and invariance on slices of the Boolean cube
• KKL, Kruskal--Katona, and Monotone Nets
• Intersecting families of permutations

This page was built for publication: Boolean degree 1 functions on some classical association schemes