Results 11 to 20 of about 2,673 (59)

New upper bound for lattice covering by spheres

Mathematika, Volume 72, Issue 1, January 2026.
Abstract We show that there exists a lattice covering of Rn$\mathbb {R}^n$ by Euclidean spheres of equal radius with density O(nlnβn)$O\big (n \ln ^{\beta } n \big)$ as n→∞$n\rightarrow \infty$, where β≔12log28πe33=1.85837….$$\begin{align*} \beta \coloneqq \frac{1}{2} \log _2 {\left(\frac{8 \pi \mathrm{e}}{3\sqrt 3}\right)}=1.85837\,\ldots . \end{align*
Jun Gao, Xizhi Liu, Oleg Pikhurko, Shumin Sun   +3 more
wiley   +1 more source

The shift‐homological spectrum and parametrising kernels of rank functions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift‐homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical.
Isaac Bird, Jordan Williamson, Alexandra Zvonareva   +2 more
wiley   +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

Centrality of star and monotone factorisations

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3567-3585, November 2025.
Abstract A factorisation problem in the symmetric group is central if conjugate permutations always have the same number of factorisations. We give the first fully combinatorial proof of the centrality of transitive star factorisations that is valid in all genera, which answers a natural question of Goulden and Jackson from 2009.
Jesse Campion Loth, Amarpreet Rattan
wiley   +1 more source

Higher rank antipodality

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Motivated by general probability theory, we say that the set S$S$ in Rd$\mathbb {R}^d$ is antipodal of rank k$k$, if for any k+1$k+1$ elements q1,…qk+1∈S$q_1,\ldots q_{k+1}\in S$, there is an affine map from convS$\mathrm{conv}\!\left(S\right)$ to the k$k$‐dimensional simplex Δk$\Delta _k$ that maps q1,…qk+1$q_1,\ldots q_{k+1}$ bijectively ...
Márton Naszódi, Zsombor Szilágyi, Mihály Weiner   +2 more
wiley   +1 more source

Crossing estimates for the Ising model on general s‐embeddings

Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.
Abstract We prove Russo–Seymour–Welsh‐type crossing estimates for the FK–Ising model on general s‐embeddings whose origami map has an asymptotic Lipschitz constant strictly smaller than 1, provided it satisfies a mild non‐degeneracy assumption. This result extends the work of Chelkak and provides a general framework to prove that the usual connection ...
Rémy Mahfouf
wiley   +1 more source

Geometric realizations of the s‐weak order and its lattice quotients

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract For an n$n$‐tuple s${\bm{s}}$ of nonnegative integers, the s${\bm{s}}$‐weak order is a lattice structure on s${\bm{s}}$‐trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the forcing order of the s${\bm{s}}$‐weak order in terms of combinatorial objects ...
Eva Philippe, Vincent Pilaud
wiley   +1 more source

Tight Distance Query Reconstruction for Trees and Graphs Without Long Induced Cycles

Random Structures &Algorithms, Volume 66, Issue 4, July 2025.
ABSTRACT Given access to the vertex set V$$ V $$ of a connected graph G=(V,E)$$ G=\left(V,E\right) $$ and an oracle that given two vertices u,v∈V$$ u,v\in V $$, returns the shortest path distance between u$$ u $$ and v$$ v $$, how many queries are needed to reconstruct E$$ E $$?
Paul Bastide, Carla Groenland
wiley   +1 more source

Watermelon configurations with wall interaction: exact and asymptotic results

, 2005
We perform an exact and asymptotic analysis of the model of $n$ vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek.
Bailey W N, Birkhoff G D, Brak R, Brak R, Brak R, Brak R, Bray A J, C Krattenthaler, Comtet L, Csáki E, Flajolet P, Forrester P J, Forrester P J, Forrester P J, Gasper G, Gessel I M, Graham R L, Gronau H-D O F, Guttmann A J, John P, Karlin S, Karlin S, Katori M, Krattenthaler C, Krattenthaler C, Krattenthaler C, Krattenthaler C, Krattenthaler C, Lindström B, Mohanty S G, Mohanty S G, Mukherji S, Petkovsek M, Rubey M, Rubey M, Sagan B E, Slater J C, Slater L J, Whittaker E T andWatson G N, Zeilberger D   +39 more
core   +2 more sources

Moduli of finite flat torsors over nodal curves

Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.
Abstract We show that log flat torsors over a family X/S$X/S$ of nodal curves under a finite flat commutative group scheme G/S$G/S$ are classified by maps from the Cartier dual of G$G$ to the log Jacobian of X$X$. We deduce that fppf torsors on the smooth fiberss of X/S$X/S$ can be extended to global log flat torsors under some regularity hypotheses.
Sara Mehidi, Thibault Poiret
wiley   +1 more source