scholarly journals On the cycle structure of Mallows permutations

2018 ◽  
Vol 46 (2) ◽  
pp. 1114-1169 ◽  
Author(s):  
Alexey Gladkich ◽  
Ron Peled
Keyword(s):  
Cycle Structure

scholarly journals Taxing Capital? Not a Bad Idea After All!

2009 ◽  
Vol 99 (1) ◽  
pp. 25-48 ◽  
Author(s):  
Juan Carlos Conesa ◽  
Sagiri Kitao ◽  
Dirk Krueger
Keyword(s):  
Income Tax ◽  
Labor Income ◽  
Income Shocks ◽  
Capital Income ◽  
Overlapping Generations Model ◽  
Cycle Structure ◽  
Tax Rate ◽  
Average Household Income ◽  
Optimal Capital

We quantitatively characterize the optimal capital and labor income tax in an overlapping generations model with idiosyncratic, uninsurable income shocks and permanent productivity differences of households. The optimal capital income tax rate is significantly positive at 36 percent. The optimal progressive labor income tax is, roughly, a flat tax of 23 percent with a deduction of $7,200 (relative to average household income of $42,000). The high optimal capital income tax is mainly driven by the life-cycle structure of the model, whereas the optimal progressivity of the labor income tax is attributable to the insurance and redistribution role of the tax system. (JEL E13, H21, H24, H25)

scholarly journals Nonexistence of Almost Moore Digraphs of Diameter Three

10.37236/811 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
J. Conde ◽  
J. Gimbert ◽  
J. Gonzàlez ◽  
J. M. Miret ◽  
R. Moreno
Keyword(s):  
Number Theory ◽  
Graph Theory ◽  
Algebraic Number ◽  
Directed Graphs ◽  
Algebraic Number Theory ◽  
Cycle Structure ◽  
Spectral Techniques ◽  
Binary Matrices ◽  
Algebraic Multiplicities ◽  
Big Pieces

Almost Moore digraphs appear in the context of the degree/diameter problem as a class of extremal directed graphs, in the sense that their order is one less than the unattainable Moore bound $M(d,k)=1+d+\cdots +d^k$, where $d>1$ and $k>1$ denote the maximum out-degree and diameter, respectively. So far, the problem of their existence has only been solved when $d=2,3$ or $k=2$. In this paper, we prove that almost Moore digraphs of diameter $k=3$ do not exist for any degree $d$. The enumeration of almost Moore digraphs of degree $d$ and diameter $k=3$ turns out to be equivalent to the search of binary matrices $A$ fulfilling that $AJ=dJ$ and $I+A+A^2+A^3=J+P$, where $J$ denotes the all-one matrix and $P$ is a permutation matrix. We use spectral techniques in order to show that such equation has no $(0,1)$-matrix solutions. More precisely, we obtain the factorization in ${\Bbb Q}[x]$ of the characteristic polynomial of $A$, in terms of the cycle structure of $P$, we compute the trace of $A$ and we derive a contradiction on some algebraic multiplicities of the eigenvalues of $A$. In order to get the factorization of $\det(xI-A)$ we determine when the polynomials $F_n(x)=\Phi_n(1+x+x^2+x^3)$ are irreducible in ${\Bbb Q}[x]$, where $\Phi_n(x)$ denotes the $n$-th cyclotomic polynomial, since in such case they become 'big pieces' of $\det(xI-A)$. By using concepts and techniques from algebraic number theory, we prove that $F_n(x)$ is always irreducible in ${\Bbb Q}[x]$, unless $n=1,10$. So, by combining tools from matrix and number theory we have been able to solve a problem of graph theory.

scholarly journals Cycle structure of iterating Redei functions

2017 ◽  
Vol 11 (2) ◽  
pp. 397-407 ◽  
Author(s):  
Claudio Qureshi ◽  
◽  
Daniel Panario ◽  
Rodrigo Martins ◽  
◽  
...  
Keyword(s):  
Cycle Structure

scholarly journals THE EVOLUTION OF THE KREBS CYCLE: A PROMISING THEME FOR MEANINGFUL BIOCHEMISTRY LEARNING IN BIOLOGY

2015 ◽  
Vol 13 ◽  
pp. 9
Author(s):  
C. Costa ◽  
E. Galembeck
Keyword(s):  
Group Discussion ◽  
Krebs Cycle ◽  
Study Guide ◽  
Atmospheric Conditions ◽  
Cycle Structure ◽  
Peer Discussion ◽  
Evolutionary View ◽  
Micro Organisms ◽  
Educational Potential ◽  
Structure And Functions

INTRODUCTION: Evolution has been recognized as a key concept for biologists. In order to motivate biology undergraduates for contents of central energetic metabolism, we addressed the Krebs cycle structure and functions to an evolutionary view. To this end, we created a study guide which contextualizes the emergence of the cyclic pathway, in light of the prokaryotic influence since early Earth anaerobic condition to oxygen rise in atmosphere. OBJECTIVES: The main goal is to highlight the educational potential of the material whose subject is scarcely covered in biochemistry textbooks. MATERIALS AND METHODS: The study guide is composed by three interrelated sections, the problem (Section 1), designed to arouse curiosity, inform and motivate students; an introductory text (Section 2) about life evolution, including early micro-organisms and Krebs cycle emergence, and questions (Section 3) for debate. The activity consisted on a peer discussion session, with instructors tutoring. The questions were designed to foster exchange of ideas in an ever-increasing level of complexity, and cover subjects from early atmospheric conditions to organization of the metabolism along the subsequent geological ages. RESULTS AND DISCUSSION: We noticed that students were engaged and motivated by the task, especially during group discussion. Based on students’ feedbacks and class observations, we learned that the material raised curiosity and stimulated discussion among peers. It brought a historical and purposeful way of dealing with difficult biochemical concepts. CONCLUSIONS: The whole experience suggests that the study guide was a stimulus for broadening comprehension of the Krebs cycle, reinforcing the evolutionary stance as an important theme for biology and biochemistry understanding. On the other hand, we do not underestimate the fact that approaching Krebs cycle from an evolutionary standpoint is a quite complex discussion for the majority of students. KEYWORDS: Evolution. Krebs cycle. Metabolism learning. Biology. ACKNOWLEDGEMENTS: We thank Capes for financial support.

scholarly journals On the cycle structure of permutation polynomials

2008 ◽  
Vol 14 (3) ◽  
pp. 593-614 ◽  
Author(s):  
Ayça Çeşmelioğlu ◽  
Wilfried Meidl ◽  
Alev Topuzoğlu
Keyword(s):  
Permutation Polynomials ◽  
Cycle Structure

scholarly journals Permutations on finite fields with invariant cycle structure on lines

2020 ◽  
Vol 88 (9) ◽  
pp. 1723-1740
Author(s):  
Daniel Gerike ◽  
Gohar M. Kyureghyan
Keyword(s):  
Finite Fields ◽  
Homogeneous Function ◽  
Cycle Structure ◽  
Parallel Lines

Abstract We study the cycle structure of permutations $$F(x)=x+\gamma f(x)$$ F ( x ) = x + γ f ( x ) on $$\mathbb {F}_{q^n}$$ F q n , where $$f :\mathbb {F}_{q^n} \rightarrow \mathbb {F}_q$$ f : F q n → F q . We show that for a 1-homogeneous function f the cycle structure of F can be determined by calculating the cycle structure of certain induced mappings on parallel lines of $$\gamma \mathbb {F}_q$$ γ F q . Using this observation we describe explicitly the cycle structure of two families of permutations over $$\mathbb {F}_{q^2}$$ F q 2 : $$x+\gamma {{\,\mathrm{Tr}\,}}(x^{2q-1})$$ x + γ Tr ( x 2 q - 1 ) , where $$q\equiv -1 \pmod 3$$ q ≡ - 1 ( mod 3 ) and $$\gamma \in \mathbb {F}_{q^2}$$ γ ∈ F q 2 , with $$\gamma ^3=-\frac{1}{27}$$ γ 3 = - 1 27 and $$x+\gamma {{\,\mathrm{Tr}\,}}\left( x^{\frac{2^{2s-1}+3\cdot 2^{s-1}+1}{3}}\right) $$ x + γ Tr x 2 2 s - 1 + 3 · 2 s - 1 + 1 3 , where $$q=2^s$$ q = 2 s , s odd and $$\gamma \in \mathbb {F}_{q^2}$$ γ ∈ F q 2 , with $$\gamma ^{(q+1)/3}=1$$ γ ( q + 1 ) / 3 = 1 .

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