1 citations · 3 across the 9 of their papers we have counts for
9 papers
Sunflower Bound with a Sub-Logarithmic Base
Junichiro Fukuyama
We show that a family of sets each of cardinality includes a -sunflower if $ |\mathcal{F}| \ge \left( \frac{c k^2 \ln m}{\ln \ln m} \right)…
Extensions of a Family for Sunflowers
Junichiro Fukuyama
This paper explores the structure of the combinatorial domain in relation to sunflowers. The previous study found some intrinsic properties of the -extension \[ Ext \left(…
The Sunflower Conjecture Proven
Junichiro Fukuyama
We demonstrate the truth of the sunflower conjecture by showing that a family of sets each of cardinality at most includes a -sunflower, if $|\mathcal{F}| > (…
Improved Bound on Sets Including No Sunflower with Three Petals
Junichiro Fukuyama
A sunflower with petals, or -sunflower, is a family of sets every two of which have a common intersection. Known since 1960, the sunflower conjecture states that a famil…
Partial-Match Queries with Random Wildcards: In Tries and Distributed Hash Tables
Junichiro Fukuyama
Consider an -bit query to a bitwise trie . A wildcard is an unspecified bit in for which the query asks the membership for both cases and . It is commo…
Distributed Selection in Time with Messages
Piotr Berman, Junichiro Fukuyama
We consider the selection problem on a completely connected network of processors with no shared memory. Each processor initially holds a given numeric item of bits allowed…
Asymptotic Improvement of the Sunflower Bound
Junichiro Fukuyama
A sunflower with a core is a family of sets such that for each two different elements and in . The well-known sunflower lemma stat…
An Alternative Proof of the Exponential Monotone Complexity of the Clique Function
Junichiro Fukuyama
In 1985, Razborov discovered a proof that the monotone circuit complexity of the clique problem is super-polynomial. Alon and Boppana improved the result into exponential lower bou…
Computing Cliques is Intractable
Junichiro Fukuyama
The class P is in fact a proper sub-class of NP. We explore topological properties of the Hamming space 2^[n] where [n]={1, 2,..., n}. With the developed theory, we show: (i) a the…