Results 21 to 30 of about 401,547 (240)
Rook placements and generalized partition varieties
Discrete Mathematics, 1997 The paper generalizes the concept of partition varieties introduced in a preceding paper by the same author. For this purpose, \(\gamma\)-compatible partitions \(\lambda\) are introduced, where \(\gamma\) is a composition of some integers. It is shown that a certain quotient space associated to such composition \(\gamma\) and partition \(\lambda\) is a
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q-Rook placements and Jordan forms of upper-triangular nilpotent matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The set of $n$ by $n$ upper-triangular nilpotent matrices with entries in a finite field $F_q$ has Jordan canonical forms indexed by partitions $λ \vdash n$. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number$ F_λ (q)$ of matrices of fixed Jordan type as a weighted sum
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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.
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The distribution and abundance of the rook corvus frugilegus L. as influenced by habitat suitability and competitive interactions. [PDF]
, 1998 Rooks (Corvus frugilegus) are colonially breeding corvids found in most agricultural landscapes. Colonies in the County Durham area tend to be clustered at distances up to 500 m, but otherwise show little pattern in terms of spacing or size.
Griffin, Larry Roy, Griffin, L.R.
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Adaptive Foam 3D Printing of Ultralight and Multifunctional Materials
Advanced Engineering Materials, EarlyView.Adaptive foam 3D printing, enabled by expandable microspheres, imparts cellular structures to thermoplastic and thermosetting polymers, manufactured through a variety of processes including fused filament fabrication, direct ink writing, digital light processing, and inkjet printing.
Nariman Rajabifar, Amir Ameli
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Letter from Ella Roper (Rook) to John Sloan, May 14, 1949
, 1949 1 leaf (single sided)Letter from Ella Roper (Rook) to John Sloan, May 14 ...
Roper, Ella (Rook)
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Advanced Engineering Materials, EarlyView.Cu and combined Cu–P microalloying refine the microstructure and enhance the nanoindentation‐derived fracture resistance of CoNiAlSi ferromagnetic shape memory alloys without suppressing the martensitic transformation. Comparative SEM, DSC, and nanoindentation results reveal that the CuP‐containing alloy provides the most balanced response, achieving ...
Mehmet Demir
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Advances in Sustainable and Wearable Textile Based Soft Robotics
Advanced Functional Materials, EarlyView.This Review examines advances in wearable textile‐based soft robotics, focusing on sustainable materials, integrated sensing, and scalable actuation. It discusses manufacturing and system integration across healthcare, assistive robotics, prosthetics, and human–machine interfaces, and highlights key challenges in circular design, including life‐cycle ...
Zahir Abbas +6 more
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Advanced Functional Materials, EarlyView.This study presents a magneto‐mechanical strategy that incorporates FP@MSCs into an aligned PCL/GelMA nerve guidance conduit. Magnetic stimulation increases membrane tension in FP@MSCs, triggering cytoskeletal remodeling, Schwann cell‐like differentiation, and TIMP1 secretion. TIMP1 activates ITGB1/CD63–FAK signaling in NE‐4C cells, increasing membrane
Xinyu Zhu +14 more
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Invisible permutations and rook placements on a Ferrers board
Discrete Mathematics, 1995 We study non-attacking rook placements on a Ferrers board by extending them to certain permutation matrices, called invisible permutations. By introducing a length function on rook placements, we define a rook length polynomial \(\text{RL}_ k(\lambda, q)\) for a given number \(k\) of rooks and a Ferrers board \(F_ \lambda\). We prove that \(\text{R}_ k(
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