Related papers: Crystal isomorphisms and Mullineux involution II
Modern applications of algebraic topology to point cloud data analysis have motivated active investigation of combinatorial clique complexes -- high-dimensional extensions of combinatorial graphs. We show that meaningful invariants of such…
A method based on the symbolic methods of the classical invariant theory is developed for a representation of elements of kernel of Weitzenb\"ok derivations.
We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…
In order to identify clusters of objects with features transformed by unknown affine transformations, we develop a Bayesian cluster process which is invariant with respect to certain linear transformations of the feature space and able to…
A novel method for crystal structure prediction, based on metadynamics and evolutionary algorithms, is presented here. This technique can be used to produce efficiently both the ground state and metastable states easily reachable from a…
An analogy between combinatorial chemistry and Monte Carlo computer simulation is pursued. Examples of how to design libraries for both materials discovery and protein molecular evolution are given. For materials discovery, the concept of…
Let k be an algebraically closed field of characteristic p>2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the symplectic group over k in terms of cap-curl diagrams under…
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…
We prove the symmetrising trace conjecture of Brou\'e, Malle and Michel for the generic Hecke algebra associated to the exceptional irreducible complex reflection group $G_{13}$. Our result completes the proof of the conjecture for the…
A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.
A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
In this article, a novel cluster analysis algorithm was employed in the study of polymer coil to globule transition via single chain Monte Carlo simulations. The algorithm, which has been recently applied in Molecular Dynamics simulations…
We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable…
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its…
Given a finitely presented group $G$, Hopf's formula expresses the second integral homology of $G$ in terms of generators and relators. We give an algorithm that exploits Hopf's formula to estimate $H_2(G;k)$, with coefficients in a finite…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…