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pro vyhledávání: '"Cheong, Gilyoung"'
Autor:
Cheong, Gilyoung, Huang, Yifeng
We prove new statistical results about the distribution of the cokernel of a random integral matrix with a concentrated residue. Given a prime $p$ and a positive integer $n$, consider a random $n \times n$ matrix $X_n$ over the ring $\mathbb{Z}_p$ of
Externí odkaz:
http://arxiv.org/abs/2310.09491
Autor:
Cheong, Gilyoung, Yu, Myungjun
Given a prime $p$, let $P(t)$ be a non-constant monic polynomial in $t$ over the ring $\mathbb{Z}_{p}$ of $p$-adic integers. Let $X_{n}$ be an $n \times n$ random matrix over $\mathbb{Z}_{p}$ with independent entries that lie in any residue class mod
Externí odkaz:
http://arxiv.org/abs/2303.09125
Given a prime $p$ and a positive integer $k$, let $\mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z})$ be the ring of $n \times n$ matrices over $\mathbb{Z}/p^{k}\mathbb{Z}$. We consider the number of solutions $X \in \mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z
Externí odkaz:
http://arxiv.org/abs/2209.03626
Autor:
Cheong, Gilyoung, Kaplan, Nathan
Let $p$ be prime and $X$ be a Haar-random $n \times n$ matrix over $\mathbb{Z}_{p}$, the ring of $p$-adic integers. Let $P_{1}(t), \dots, P_{l}(t) \in \mathbb{Z}_{p}[t]$ be monic polynomials of degree at most $2$ whose images modulo $p$ are distinct
Externí odkaz:
http://arxiv.org/abs/2201.08777
Autor:
Cheong, Gilyoung, Huang, Yifeng
Given an elliptic curve $E$ defined over $\mathbb{C}$, let $E^{\times}$ be an open subset of $E$ obtained by removing a point. In this paper, we show that the $i$-th Betti number of the unordered configuration space $\mathrm{Conf}^{n}(E^{\times})$ of
Externí odkaz:
http://arxiv.org/abs/2009.07976
Given a positive integer $r$ and a prime power $q$, we estimate the probability that the characteristic polynomial $f_{A}(t)$ of a random matrix $A$ in $\mathrm{GL}_{n}(\mathbb{F}_{q})$ is square-free with $r$ (monic) irreducible factors when $n$ is
Externí odkaz:
http://arxiv.org/abs/2005.07846
Autor:
Cheong, Gilyoung
We generalize a formula due to Macdonald that relates the singular Betti numbers of $X^{n}/G$ to those of $X$, where $X$ is a compact manifold and $G$ is any subgroup of the symmetric group $S_{n}$ acting on $X^{n}$ by permuting coordinates. Our resu
Externí odkaz:
http://arxiv.org/abs/2003.04825
Publikováno v:
In Linear Algebra and Its Applications 15 November 2023 677:1-30
Autor:
Cheong, Gilyoung, Huang, Yifeng
Let $(R, \mathfrak{m})$ be a complete discrete valuation ring with the finite residue field $R/\mathfrak{m} = \mathbb{F}_{q}$. Given a monic polynomial $P(t) \in R[t]$ whose reduction modulo $\mathfrak{m}$ gives an irreducible polynomial $\bar{P}(t)
Externí odkaz:
http://arxiv.org/abs/1812.11728
Publikováno v:
In Linear Algebra and Its Applications 15 December 2022 655:100-128