2 citations · 2 across the 6 of their papers we have counts for
7 papers
Caps and LCD Codes with Large Dimensions
Keita Ishizuka, Yuhi Kamio
We establish a connection between linear complementary dual (LCD) codes and caps in projective space. Using this framework and the structure theory of maximal binary caps, we deriv…
Lawvere's fourth open problem: Levels in the topos of symmetric simplicial sets
Ryuya Hora, Yuhi Kamio, Yuki Maehara
In the topos of simplicial sets, it makes sense to ask the following question about a given natural number : what is the minimum value such that -skeletality implies -…
Asymptotic Analysis of Infinite Decompositions of a Unit Fraction into Unit Fractions
Yuhi Kamio
Paul Erdős posed a problem on the asymptotic estimation of decomposing 1 into a sum of infinitely many unit fractions in \cite{Erd80}. We point out that this problem can be solved…
Solution to Lawvere's first problem: a Grothendieck topos that has proper class many quotient topoi
Yuhi Kamio, Ryuya Hora
This paper solves the first of the open problems in topos theory posted by William Lawvere, concerning the existence of a Grothendieck topos that has proper class many quotient top…
The bounds of rigid sphere design
Yuhi Kamio
We have identified some necessary conditions for the existence of rigid sphere designs. In particular, we have successfully resolved the conjecture proposed by [Ban87]; Given fixed…
Quadratic residues and domino tilings
Yuhi Kamio, Junnosuke Koizumi, Toshihiko Nakazawa
The formula for the number of domino tilings due to Kasteleyn and Temperley-Fisher is strikingly similar to Eisenstein's formula for the Legendre symbol. We study the connection be…
Quotient toposes of discrete dynamical systems
Ryuya Hora, Yuhi Kamio
This paper gives a classification of classes of discrete dynamical systems (a set equipped with an endofunction) closed under finite limits and small colimits. The conclusion is si…