Results 51 to 60 of about 74,505 (227)

Hurwitz numbers for reflection groups III: Uniform formulae

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We give uniform formulae for the number of full reflection factorizations of a parabolic quasi‐Coxeter element in a Weyl group or complex reflection group, generalizing the formula for the genus‐0 Hurwitz numbers. This paper is the culmination of a series of three.
Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Morales   +2 more
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

Unlocking Transplant Tolerance with Biomaterials

Advanced Healthcare Materials, Volume 14, Issue 5, February 18, 2025.
Transplantation holds great promise, but the lack of long‐term success outcomes highlights the need for more targeted therapeutics and insights from immune rejection mechanisms. This review delves into how biomaterials offer a versatile toolbox for engineering next‐generation therapeutics, emphasizing the inherent properties of materials that suit ...
John‐Paul A. Pham, María M. Coronel
wiley   +1 more source

C-Finite Sequences and Riordan Arrays

Mathematics
Many 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
doaj   +1 more source

Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract We prove a universal substitution formula that compares generating series of Euler characteristics of Nakajima quiver varieties associated with affine ADE diagrams at generic and at certain non‐generic stability conditions via a study of collapsing fibres in the associated variation of GIT map, unifying and generalising earlier results of the ...
Lukas Bertsch, Ádám Gyenge, Balázs Szendrői   +2 more
wiley   +1 more source

Partial $γ$-Positivity for Quasi-Stirling Permutations of Multisets [PDF]

arXiv, 2021
We prove that the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents are partial $\gamma$-positive, thereby confirming a recent conjecture posed by Lin, Ma and Zhang. This is accomplished by proving the partial $\gamma$-positivity of the enumerative polynomials of certain
arxiv  

On the real‐rootedness of the Eulerian transformation

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract The Eulerian transformation is the linear operator on polynomials in one variable with real coefficients that maps the powers of this variable to the corresponding Eulerian polynomials. The derangement transformation is defined similarly.
Christos A. Athanasiadis
wiley   +1 more source

Central limit theorem in disordered Monomer‐Dimer model

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
Abstract We consider the disordered monomer‐dimer model on general finite graphs with bounded degrees. Under the finite fourth moment assumption on the weight distributions, we prove a Gaussian central limit theorem for the free energy of the associated Gibbs measure with a rate of convergence. The central limit theorem continues to hold under a nearly
Wai‐Kit Lam, Arnab Sen
wiley   +1 more source

Enumerative properties of generalized associahedra [PDF]

arXiv, 2004
Some enumerative aspects of the fans, called generalized associahedra, introduced by S. Fomin and A. Zelevinsky in their theory of cluster algebras are considered, in relation with a bicomplex and its two spectral sequences. A precise enumerative relation with the lattices of generalized noncrossing partitions is conjectured and some evidence is given.
arxiv  

A Sharp Threshold for a Random Version of Sperner's Theorem

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT The Boolean lattice 𝒫(n) consists of all subsets of [n]={1,…,n}$$ \left[n\right]=\left\{1,\dots, n\right\} $$ partially ordered under the containment relation. Sperner's Theorem states that the largest antichain of the Boolean lattice is given by a middle layer: the collection of all sets of size n/2$$ \left\lfloor n/2\right\rfloor $$, or also,
József Balogh, Robert A. Krueger
wiley   +1 more source