scholarly journals On conjectures regarding the Nekrasov–Okounkov hook length formula

2019 ◽  
Vol 113 (4) ◽  
pp. 355-366 ◽  
Author(s):  
Bernhard Heim ◽  
Markus Neuhauser
Keyword(s):  
Hook Length

scholarly journals The role of the FliK molecular ruler in hook-length control inSalmonella enterica

2010 ◽  
Vol 75 (5) ◽  
pp. 1272-1284 ◽  
Author(s):  
Marc Erhardt ◽  
Takanori Hirano ◽  
Yichu Su ◽  
Koushik Paul ◽  
Daniel H. Wee ◽  
...  
Keyword(s):  
Hook Length ◽  
Molecular Ruler

scholarly journals On the growth and zeros of polynomials attached to arithmetic functions

2021 ◽  
Author(s):  
Bernhard Heim ◽  
Markus Neuhauser
Keyword(s):  
Lie Algebras ◽  
Chebyshev Polynomials ◽  
Fourier Coefficients ◽  
Arithmetic Functions ◽  
Zeros Of Polynomials ◽  
Simple Complex ◽  
Hook Length ◽  
Moderate Growth ◽  
Growth Properties ◽  
Sum Of Divisors

AbstractIn this paper we investigate growth properties and the zero distribution of polynomials attached to arithmetic functions g and h, where g is normalized, of moderate growth, and $$0<h(n) \le h(n+1)$$ 0 < h ( n ) ≤ h ( n + 1 ) . We put $$P_0^{g,h}(x)=1$$ P 0 g , h ( x ) = 1 and $$\begin{aligned} P_n^{g,h}(x) := \frac{x}{h(n)} \sum _{k=1}^{n} g(k) \, P_{n-k}^{g,h}(x). \end{aligned}$$ P n g , h ( x ) : = x h ( n ) ∑ k = 1 n g ( k ) P n - k g , h ( x ) . As an application we obtain the best known result on the domain of the non-vanishing of the Fourier coefficients of powers of the Dedekind $$\eta $$ η -function. Here, g is the sum of divisors and h the identity function. Kostant’s result on the representation of simple complex Lie algebras and Han’s results on the Nekrasov–Okounkov hook length formula are extended. The polynomials are related to reciprocals of Eisenstein series, Klein’s j-invariant, and Chebyshev polynomials of the second kind.

FliK, the protein responsible for flagellar hook length control in Salmonella, is exported during hook assembly

1999 ◽  
Vol 34 (2) ◽  
pp. 295-304 ◽  
Author(s):  
Tohru Minamino ◽  
Bertha Gonzalez-Pedrajo ◽  
Kenta Yamaguchi ◽  
Shin-Ichi Aizawa ◽  
Robert M. Macnab
Keyword(s):  
Hook Length

scholarly journals Roles of FliK and FlhB in determination of flagellar hook length in Salmonella typhimurium.

1994 ◽  
Vol 176 (17) ◽  
pp. 5439-5449 ◽  
Author(s):  
T Hirano ◽  
S Yamaguchi ◽  
K Oosawa ◽  
S Aizawa
Keyword(s):  
Salmonella Typhimurium ◽  
Hook Length

scholarly journals On an identity of Glass and Ng concerning the hook length formula

2010 ◽  
Vol 310 (17-18) ◽  
pp. 2440-2442
Author(s):  
Rong Zhang
Keyword(s):  
Hook Length
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