Let a=(ai) i≥ 1 be a sequence in a field F, and f: F× F→ F be a function such that f (ai, ai)≠ 0
for all i≥ 1. For any tournament T over [n], consider the n× n symmetric matrix MT with zero …

For a set $ L $ of positive proper fractions and a positive integer $ r\geq 2$, a fractional $ r $-
closed $ L $-intersecting family is a collection $\mathcal {F}\subset\mathcal {P}([n]) $ with the …

Suppose F is a field and let a≔(a 1, a 2,…) be a sequence of non-zero elements in F. For
an≔(a 1,…, an), we consider the family M n (a) of n× n symmetric matrices M over F with all …

Using the sunflower method, we show that if $\theta\in (0, 1)\cap\mathbb {Q} $ and $\mathcal
{F} $ is a $ O (n^{1/3}) $-bounded $\theta $-intersecting family over $[n] $, then …

Let F be a field and suppose a:=(a 1, a 2,…) is a sequence of non-zero elements in F. For a
tournament T on [n], associate the n× n symmetric matrix MT (a)(resp. skew-symmetric matrix …

In the first part of this paper, we prove a theorem which is the $ q $-analogue of a
generalized modular Ray-Chaudhuri-Wilson Theorem shown in [Alon, Babai, Suzuki, J …

Abstract Let A={A_ 1, ..., A_ p\} A= A 1,…, A p and B={B_ 1, ..., B_ q\} B= B 1,…, B q be two
families of subsets of n such that for every i ∈ pi∈ p and j ∈ qj∈ q,| A_ i ∩ B_ j|= cd| B_ j|| A …

Given an irreducible fraction cd∈[0, 1], a pair (A, B) is called acd-cross-intersecting pair of 2
[n] if A, B are two families of subsets of [n] such that for every pair A∈ A and B∈ B,| A∩ B …

Let $ L=\{\frac {a_1}{b_1},\ldots,\frac {a_s}{b_s}\} $, where for every $ i\in [s] $, $\frac
{a_i}{b_i}\in [0, 1) $ is an irreducible fraction. Let $\mathcal {F}=\{A_1,\ldots, A_m\} $ be a …

Abstract Let A={A1,..., Ap} and B={B1,..., Bq} be two families of subsets of [n] such that for
every i∈[p] and j∈[q],| Ai∩ Bj|= cd| Bj|, where cd∈[0, 1] is an irreducible fraction. We call …