Results 11 to 20 of about 590,558 (231)
Rook placements in $G_2$ and $F_4$ and associated coadjoint orbits [PDF]
Communications in Mathematics, 2023 Let $\mathfrak{n}$ be a maximal nilpotent subalgebra of a simple complex Lie algebra with root system $\Phi$. A subset $D$ of the set $\Phi^+$ of positive roots is called a rook placement if it consists of roots with pairwise non-positive scalar products. To each rook placement $D$ and each map $\xi$ from $D$ to the set $\mathbb{C}^{\times}$ of nonzero
Ignatev, Mikhail V., Surkov, Matvey A.
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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
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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 ...
P. Hanlon
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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
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Proceedings of the American Mathematical Society18 ...
Ignatev, Mikhail, Venchakov, Mikhail
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Combinatorial Insights into Numerical Semigroups: Rook Placements and Lah Numbers
Turkish Journal of Science and TechnologyThis paper investigates the interplay between numerical semigroups and enumerative combinatorics through the lens of Young diagrams, rook polynomials, and the Lah numbers. For a given numerical semigroup S, we associate a Young diagram constructed from the gap set of S.
Meral Süer
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Discovery of VU6052254: A Novel, Potent M<sub>1</sub> Positive Allosteric Modulator. [PDF]
ACS Chem NeurosciWe recently disclosed VU0467319, a muscarinic acetylcholine receptor subtype 1 (M1) Positive Allosteric Modulator (PAM) clinical candidate that had successfully completed a Phase I Single Ascending Dose (SAD) clinical trial, but the identification of an ...
Engers JL +19 more
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A generalization of Eulerian numbers via rook placements [PDF]
Involve, a Journal of Mathematics, 2017 15 ...
Banaian, Esther +5 more
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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
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Matrix Ansatz, lattice paths and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP. Besides other interpretations, this formula gives the generating function for permutations of a given size with ...
Corteel, S. +3 more
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