Results 21 to 30 of about 52 (52)

Fundamental motifs and parity within the crystallographic point groups

Journal of Applied Crystallography, Volume 58, Issue 4, Page 1447-1454, August 2025.
The Hasse diagram of the 3D point‐group classes is built with six motifs that have a well defined parity that determines their structure. Of the seven crystal systems, three are built with odd motifs, three are built with even motifs and the last one, the monoclinics, is `ambidextrous' as they are built with both.This paper analyzes the Hasse diagram ...
Maureen M. Julian, Matthew Macauley
wiley   +1 more source

The birational geometry of GIT quotients

Bulletin of the London Mathematical Society, Volume 57, Issue 7, Page 1952-1967, July 2025.
Abstract Geometric invariant theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev–Hu and Thaddeus, it is known that two quotients of the same variety using different polarisations are related by birational transformations.
Ruadhaí Dervan, Rémi Reboulet
wiley   +1 more source

Generic root counts and flatness in tropical geometry

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We use tropical and nonarchimedean geometry to study the generic number of solutions of families of polynomial equations over a parameter space Y$Y$. In particular, we are interested in the choices of parameters for which the generic root count is attained.
Paul Alexander Helminck, Yue Ren
wiley   +1 more source

Basilica: New canonical decomposition in matching theory

Journal of Graph Theory, Volume 108, Issue 3, Page 508-542, March 2025.
Abstract In matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are ...
Nanao Kita
wiley   +1 more source

The Shi variety corresponding to an affine Weyl group

Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 913-940, March 2025.
Abstract Let W$W$ be an irreducible Weyl group and Wa$W_a$ its affine Weyl group. In this article we show that there exists a bijection between Wa$W_a$ and the integral points of an affine variety, denoted X̂Wa$\widehat{X}_{W_a}$, which we call the Shi variety of Wa$W_a$.
Nathan Chapelier‐Laget
wiley   +1 more source

On the parameterized Tate construction

Journal of Topology, Volume 18, Issue 1, March 2025.
Abstract We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension Ĝ$\widehat{G}$ of a finite group G$G$ by a compact Lie group K$K$, which we call the parameterized Tate construction (−)tGK$(-)^{t_G K}$.
J. D. Quigley, Jay Shah
wiley   +1 more source

Steenrod operations via higher Bruhat orders

Proceedings of the London Mathematical Society, Volume 130, Issue 2, February 2025.
Abstract The purpose of this paper is to establish a correspondence between the higher Bruhat orders of Yu. I. Manin and V. Schechtman, and the cup‐i$i$ coproducts defining Steenrod squares in cohomology. To any element of the higher Bruhat orders, we associate a coproduct, recovering Steenrod's original ones from extremal elements in these orders ...
Guillaume Laplante‐Anfossi, Nicholas J. Williams   +1 more
wiley   +1 more source

CAT(0) and cubulated Shephard groups

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well‐known result that Coxeter groups are CAT(0)$\mathrm{CAT}(0)$ to a class of Shephard ...
Katherine M. Goldman
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, Joshua Maglione, Christian Stump   +2 more
wiley   +1 more source