Kota Saito

activity

20172023

most citedApproximate Expected Utility Rationalization

4 citations · 13 across the 17 of their papers we have counts for

collaborators

18 papers

math.NT2023

Finiteness of solutions to linear Diophantine equations on Piatetski-Shapiro sequences

Kota Saito

A sequence of integers of the form $⌊ n^{α} ⌋$ $(n = 1, 2, \dots)$ for some fixed non-integral $α > 1$ is called a Piatetski-Shapiro sequence, where $⌊ x ⌋$ denotes…

econ.TH2023

Random Utility with Unobservable Alternatives

Haruki Kono, Kota Saito, Alec Sandroni

The random utility model, a cornerstone in economics, is axiomatized by Falmagne (1978) and McFadden and Richter (1990) with the assumption that if a menu is observable, the choice…

math.CO2022★ 1 cited

Adjacencies on random ordering polytopes and flow polytopes

Jean-Paul Doignon, Kota Saito

The Multiple Choice Polytope (MCP) is the prediction range of a random utility model due to Block and Marschak (1960). Fishburn (1998) offers a nice survey of the findings on rando…

math.NT2022

A system of certain linear Diophantine equations on analogs of squares

Yuya Kanado, Kota Saito

This study investigates the existence of tuples $(k, ℓ, m)$ of integers such that all of $k$ , $ℓ$ , $m$ , $k + ℓ$ , $ℓ + m$ , $m + k$ , $k + ℓ + m$ belong to $S (α)$ , where $S (α)$ i…

econ.TH2022★ 1 cited

Approximating Choice Data by Discrete Choice Models

Haoge Chang, Yusuke Narita, Kota Saito

We obtain a necessary and sufficient condition under which random-coefficient discrete choice models, such as mixed-logit models, are rich enough to approximate any nonparametric r…

math.NT2021★ 1 cited

Topological properties and algebraic independence of sets of prime-representing constants

Kota Saito, Wataru Takeda

Let $(c_{k})_{k \in N}$ be a sequence of positive integers. We investigate the set of $A > 1$ such that the integer part of $A^{c_{1} \dots c_{k}}$ is always a prime number for eve…

econ.GN2021★ 4 cited

Approximate Expected Utility Rationalization

Federico Echenique, Kota Saito, Taisuke Imai

We propose a new measure of deviations from expected utility theory. For any positive number~ $e$ , we give a characterization of the datasets with a rationalization that is within~$…

math.NT2021

Prime-representing functions and Hausdorff dimension

Kota Saito

In 2010, Matomäki investigated the set of $A > 1$ such that the integer part of $A^{c^{k}}$ is a prime number for every $k \in N$ , where $c \geq 2$ is any fixed real number. S…

math.NT2020

Linear equations with two variables in Piatetski-Shapiro sequences

Kota Saito

For every non-integral $α > 1$ , the sequence of the integer parts of $n^{α}$ $(n = 1, 2, \dots)$ is called the Piatetski-Shapiro sequence with exponent $α$ , and let $PS (α)$ denot…

math.NT2020★ 1 cited

Linear Diophantine equations in Piatetski-Shapiro sequences

Toshiki Matsusaka, Kota Saito

A Piatetski-Shapiro sequence with exponent $α$ is a sequence of integer parts of $n^{α}$ $(n = 1, 2, \dots)$ with a non-integral $α > 0$ . We let $PS (α)$ denote the set of thos…

math.NT2020★ 2 cited

Distributions of Finite Sequences Represented by Polynomials in Piatetski-Shapiro Sequences

Kota Saito, Yuuya Yoshida

By using the work of Frantzikinakis and Wierdl, we can see that for all $d \in N$ , $α \in (d, d + 1)$ , and integers $k \geq d + 2$ and $r \geq 1$ , there exist infinitely many $n\in\math…

math.NT2020

Transcendence of values of the iterated exponential function at algebraic points

Hirotaka Kobayashi, Kota Saito, Wataru Takeda

We say that the order of an algebraic number $A$ is the minimum of positive integers $k$ such that $A^{k}$ is rational. In this paper, we show that the number of algebraic numbers $A…

math.CA2019★ 1 cited

New bounds for dimensions of a set uniformly avoiding multi-dimensional arithmetic progressions

Kota Saito

Let $r_{k} (N)$ be the largest cardinality of a subset of ${1, \dots, N}$ which does not contain any arithmetic progressions (APs) of length $k$ . In this paper, we give new upper and…

math.HO2018

A fractal proof of the infinitude of primes

Kota Saito

This short paper gives another proof of the infinitude of primes by using upper box dimension, which is one of fractal dimensions.

math.NT2018★ 2 cited

Arithmetic Progressions in the Graphs of Slightly Curved Sequences

Kota Saito, Yuuya Yoshida

A strictly increasing sequence of positive integers is called a slightly curved sequence with small error if the sequence can be well-approximated by a function whose second deriva…

math.CA2018

Construction of a one-dimensional set which asymptotically and omnidirectionally contains arithmetic progressions

Kota Saito

In this paper, we construct a subset of $R^{d}$ which asymptotically and omnidirectionally contains arithmetic progressions but has Assouad dimension 1. More precisely, we s…

math.NT2018

New fractal dimensions and some applications to arithmetic patches

Kota Saito

In this paper, we define new fractal dimensions of a metric space in order to calculate the roughness of a set on a large scale. These fractal dimensions are called upper zeta dime…

math.CA2017

Dimensions of sets which uniformly avoid arithmetic progressions

Jonathan M. Fraser, Kota Saito, Han Yu

We provide estimates for the dimensions of sets in $R$ which uniformly avoid finite arithmetic progressions. More precisely, we say $F$ uniformly avoids arithmetic progres…