M.E. Mays and J. Wojciechowski. A determinant property of Catalan numbers. Discrete Mathematics, 211(1-3):125-134, 2000.M. E. Mays and J. Wojciechowski. A determinant property of Catalan numbers. Discrete Mathematics, 211(1-3):125-134, 2000....
aWe wish to present a simple combinatorial proof of a determinant formula connecting the Catalan numbers and a matrix derived from Pascal's triangle. We prove the formula by counting perfect matchings in a suitably chosen class of graphs. Although the proof relies on results and techniques from ...
One important property is the density of MPs, which can affect the vertical distribution and mobility of MP in the water column, subsequently affecting the process of microbial colonization (Stabnikova et al. 2021; Shamskhany et al. 2021). MPs with a lower density than water (e.g., PP, ...
H. Lehmer'sTridiagonal Determinant: An Étude in (Andrews-Inspired) Experimental Mathematics. 363.Formichella, Sam; Straub, Armin: Gaussian BinomialCoefficients with Negative Arguments. 371.Fu, Shishuo; Tang, Dazhao; Yee, Ae Ja: A Lecture HallTheorem for m-Falling Partitions. 395.Garvan, ...
L. Lanyon Functional strain as a determinant for bone remodeling Calcif. Tissue Int., 36 (1) (1984), pp. S56-S61 View PDFView articleView in ScopusGoogle Scholar [142] B. Behrens, A. Bouguecha, I. Nolte, A. Meyer-Lindenberg, C. Stukenborg-Colsman, T. Pressel Strain adaptive bone...
Cofactor as derivative of determinant Homology, the big picture Legal Systems very different from ours Shrinking wedge of circles / Hawaiian earring (TODO) Simplicial approxmation of maps (TODO) Lebesgue number lemma (TODO) Lean internals Cheat Sheet MicroUI Proof of tree having (V-1...
Determining the safety and biocompatibility of MSNs is crucial owing to its variable characteristics. The data generated from literature suggest that careful control of particle size and shape is the determinant factor in the biodistribution and toxicity of MSNs. In addition, the safety and toxicity ...
In this note we introduce a determinant and then give its evaluating formula. The determinant turns out to be a generalization of the well-known ballot and Fuss-Catalan numbers, which is believed to be new. The evaluating formula is proved by showing that the determinant coincides with the ...
A determinant representation for generalized ballot and Fuss-Catalan numbersMathematics - CombinatoricsJames J.Y. ZhaoarXiv
Orthogonal polynomials, Catalan numbers, and a general Hankel determinant evaluation. Linear Algebra and Its Applications . 2012; 436 (7):2105–2116.W. Chammam, F. Marcellan, and R. Sfaxi, Orthogonal polynomials, Catalan numbers, and a general Hankel determinant evaluation, Linear Alg. Appl. ...