Aimed at graduate students and researchers, this fascinating text provides a comprehensive
study of the Erdős–Ko–Rado Theorem, with a focus on algebraic methods. The authors …

Extremal set theory is dealing with families, F of subsets of an n-element set. The usual
problem is to determine or estimate the maximum possible size of F, supposing that F …

Let n and t be positive integers with t< n, and let q be a prime power. A partial (t− 1)-spread
of PG (n− 1, q) is a set of (t− 1)-dimensional subspaces of PG (n− 1, q) that are pairwise …

Cameron–Liebler sets of k-spaces were introduced recently in Filmus and Ihringer (J
Combin Theory Ser A, 2019). We list several equivalent definitions for these Cameron …

We look at a generalization of Cameron-Liebler line classes to sets of k-spaces, focusing on
results in PG (2 k+ 1, q). Here we obtain a connection to k-spreads which parallels the …

The study of intersecting structures is central to extremal combinatorics. A family of
permutations F⊂ S n is t-intersecting if any two permutations in F agree on some t indices …

We show that the q-Kneser graph qK 2 k: k (the graph on the k-subspaces of a 2 k-space
over GF (q), where two k-spaces are adjacent when they intersect trivially), has chromatic …

Abstract The notion of Cameron–Liebler line classes was generalized in Rodgers et
al.(0000) to Cameron–Liebler k-classes, where k= 1 corresponds to the line classes. Such a …

Let be a ring and be the set of all non-trivial left ideals of. The intersection graph of ideals of,
denoted by, is a graph with the vertex set and two distinct vertices and are adjacent if and …

Let V be an n-dimensional vector space over a q-element field. For an integer t≥ 2, a family
F of k-dimensional subspaces in V is t-intersecting if dim⁡(F 1∩ F 2)≥ t for any F 1, F 2∈ F …