scholarly journals Bruhat Order on Partial Fixed Point Free Involutions

10.37236/4396 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Mahir Bilen Can ◽  
Yonah Cherniavsky ◽  
Tim Twelbeck
Keyword(s):  
Fixed Point ◽  
Zeta Function ◽  
Finite Fields ◽  
Generating Function ◽  
Bruhat Order ◽  
Symmetric Matrices ◽  
Order Complex ◽  
Orbit Closures

The order complex of inclusion poset $PF_n$ of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that $PF_n$ is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of $PF_n$ is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.

scholarly journals A new generating function for calculating the Igusa local zeta function

2017 ◽  
Vol 304 ◽  
pp. 355-420 ◽  
Author(s):  
Raemeon A. Cowan ◽  
Daniel J. Katz ◽  
Lauren M. White
Keyword(s):  
Zeta Function ◽  
Generating Function ◽  
Local Zeta Function

scholarly journals MOTIVIC HILBERT ZETA FUNCTIONS OF CURVES ARE RATIONAL

2018 ◽  
Vol 19 (3) ◽  
pp. 947-964
Author(s):  
Dori Bejleri ◽  
Dhruv Ranganathan ◽  
Ravi Vakil
Keyword(s):  
Zeta Function ◽  
Generating Function ◽  
Zeta Functions ◽  
Hilbert Schemes ◽  
Grothendieck Ring

The motivic Hilbert zeta function of a variety $X$ is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points on $X$. In this paper, the motivic Hilbert zeta function of a reduced curve is shown to be rational.

scholarly journals A Dirichlet series expansion for the p-adic zeta-function

2006 ◽  
Vol 81 (2) ◽  
pp. 215-224 ◽  
Author(s):  
Daniel Delbourgo
Keyword(s):  
Fractional Derivative ◽  
Zeta Function ◽  
Dirichlet Series ◽  
Series Expansion ◽  
Generating Function

AbstractWe prove that the p-adic zeta-function constructed by Kubota and Leopoldt has the Dirichlet series expansion Where the convergence of the first summation is for the p-adic topology. The proof of this formula relates the values of p(–s, ω1+σ) for s ∈ Zp, with a branch of the ‘sth-fractional derivative’, of a suitable generating function.

scholarly journals Derangements in cosets of primitive permutation groups

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Andrei Pavelescu
Keyword(s):  
Fixed Point ◽  
Finite Fields ◽  
Permutation Groups ◽  
Normal Subgroups ◽  
Primitive Groups ◽  
Branched Coverings ◽  
Affine Groups ◽  
Nonabelian Subgroup ◽  
Projective Curves ◽  
Curves Over Finite Fields

AbstractMotivated by questions arising in connection with branched coverings of connected smooth projective curves over finite fields, we study the proportion of fixed-point free elements (derangements) in cosets of normal subgroups of primitive permutations groups. Using the Aschbacher–O'Nan–Scott Theorem for primitive groups to partition the problem, we provide complete answers for affine groups and groups which contain a regular normal nonabelian subgroup.

scholarly journals Pairs of Quadratic Forms over Finite Fields

10.37236/4072 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Alexander Pott ◽  
Kai-Uwe Schmidt ◽  
Yue Zhou
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Boolean Functions ◽  
Quadratic Forms ◽  
Symmetric Matrices ◽  
Explicit Expressions

Let $\mathbb{F}_q$ be a finite field with $q$ elements and let $X$ be a set of matrices over $\mathbb{F}_q$. The main results of this paper are explicit expressions for the number of pairs $(A,B)$ of matrices in $X$ such that $A$ has rank $r$, $B$ has rank $s$, and $A+B$ has rank $k$ in the cases that (i) $X$ is the set of alternating matrices over $\mathbb{F}_q$ and (ii) $X$ is the set of symmetric matrices over $\mathbb{F}_q$ for odd $q$. Our motivation to study these sets comes from their relationships to quadratic forms. As one application, we obtain the number of quadratic Boolean functions that are simultaneously bent and negabent, which solves a problem due to Parker and Pott.

A fixed-point property for Galton–Watson processes with generation dependence

1981 ◽  
Vol 18 (02) ◽  
pp. 514-519
Author(s):  
Dean H. Fearn
Keyword(s):  
Fixed Point ◽  
Generating Function ◽  
Probability Generating Function ◽  
Fixed Point Property ◽  
Point Property

Conditions for the non-sure extinction of Galton-Watson processes with generation dependence are obtained. Also a condition is given for such processes to have a strictly increasing probability generating function.

scholarly journals Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs

2018 ◽  
Vol 07 (03) ◽  
pp. 1850007
Author(s):  
O. Khorunzhiy
Keyword(s):  
Graph Theory ◽  
Zeta Function ◽  
Long Range ◽  
Riemann Hypothesis ◽  
Counting Function ◽  
Symmetric Matrices ◽  
Ihara Zeta Function ◽  
Unique Measure ◽  
Edge Probability ◽  
Average Vertex

We consider the ensemble of [Formula: see text] real random symmetric matrices [Formula: see text] obtained from the determinant form of the Ihara zeta function associated to random graphs [Formula: see text] of the long-range percolation radius model with the edge probability determined by a function [Formula: see text]. We show that the normalized eigenvalue counting function of [Formula: see text] weakly converges in average as [Formula: see text], [Formula: see text] to a unique measure that depends on the limiting average vertex degree of [Formula: see text] given by [Formula: see text]. This measure converges in the limit of infinite [Formula: see text] to a shift of the Wigner semi-circle distribution. We discuss relations of these results with the properties of the Ihara zeta function and weak versions of the graph theory Riemann Hypothesis.

A fixed-point property for Galton–Watson processes with generation dependence

1981 ◽  
Vol 18 (2) ◽  
pp. 514-519 ◽  
Author(s):  
Dean H. Fearn
Keyword(s):  
Fixed Point ◽  
Generating Function ◽  
Probability Generating Function ◽  
Fixed Point Property ◽  
Point Property

Conditions for the non-sure extinction of Galton-Watson processes with generation dependence are obtained. Also a condition is given for such processes to have a strictly increasing probability generating function.

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