Results 21 to 30 of about 2,345 (191)
On a dispersion problem in grid labeling [PDF]
, 2012 International audienceGiven $k$ labelings of a finite $d$-dimensional cubical grid, define the combined distance between two labels to be the sum of the $l_1$-distance between the two labels in each labeling.
Jiang, Minghui +2 more
core +4 more sources
The Matrix Ansatz, Orthogonal Polynomials, and Permutations [PDF]
, 2010 In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We illustrate this
Corteel, Sylvie +2 more
core +4 more sources
A random walk on the rook placements on a Ferrer's board [PDF]
The Electronic Journal of Combinatorics, 1996 Let $B$ be a Ferrers board, i.e., the board obtained by removing the Ferrers diagram of a partition from the top right corner of an $n\times n$ chessboard. We consider a Markov chain on the set $R$ of rook placements on $B$ in which you can move from one placement to any other legal placement obtained by switching the columns in which two rooks ...
openaire +2 more sources
Bijections on
European Journal of Combinatorics, 2016 Suppose the rows of a board are partitioned into sets of m rows called levels. An m-level rook placement is a subset of the board where no two squares are in the same column or the same level. We construct explicit bijections to prove three theorems about such placements.
Kenneth Barrese +3 more
openaire +2 more sources
Combinatorics of $B$-orbits and Bruhat--Chevalley order on involutions [PDF]
, 2011 Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.
A Melnikov +17 more
core +1 more source
Rook Placements in An and Combinatorics of B-Orbit Closures
Journal of Lie Theory, 2014 Let $G$ be a complex reductive group, $B$ be a Borel subgroup of G, $\nt$ be the Lie algebra of the unipotent radical of $B$, and $\nt^*$ be its dual space. Let $Φ$ be the root system of $G$, and $Φ^+$ be the set of positive roots with respect to $B$. A subset of $Φ^+$ is called a rook placement if it consists of roots with pairwise non-positive inner ...
Ignatyev, Mikhail V. +1 more
openaire +3 more sources
Bijection Between Increasing Binary Trees and Rook Placements on Double Staircases
The Electronic Journal of Combinatorics, 2023 In this paper, we shall construct a bijection between rook placements on double staircases (introduced by Josuat-Vergès in 2017) and increasing binary trees. We introduce two subclasses of rook placements on double staircases, which we call left and right-aligned rook placements.
openaire +2 more sources
Partitions of Matrix Spaces With an Application to $q$-Rook Polynomials
, 2019 We study the row-space partition and the pivot partition on the matrix space $\mathbb{F}_q^{n \times m}$. We show that both these partitions are reflexive and that the row-space partition is self-dual.
Gluesing-Luerssen, Heide +1 more
core +1 more source
Advanced Functional Materials, EarlyView.This study presents novel anti‐counterfeiting tags with multilevel security features that utilize additional disguise features. They combine luminescent nanosized Ln‐MOFs with conductive polymers to multifunctional mixed‐matrix membranes and powder composites. The materials exhibit visible/NIR emission and matrix‐based conductivity even as black bodies.
Moritz Maxeiner +9 more
wiley +1 more source