ﻻ يوجد ملخص باللغة العربية
A notion of $t$-designs in the symmetric group on $n$ letters was introduced by Godsil in 1988. In particular $t$-transitive sets of permutations form a $t$-design. We derive special lower bounds for $t=1$ and $t=2$ by a power moment method. For general $n,t$ we give a %linear programming lower bound . For $nge 4$ and $t=2,$ this bound is strong enough to show a lower bound on the size of such $t$-designs of $n(n-1)dots (n-t+1),$ which is best possible when sharply $t$-transitive sets of permutations exist. This shows, in particular, that tight $2$-designs do not exist.
We give two combinatorial proofs of Goulden and Jacksons formula for the number of minimal transitive factorizations of a permutation when the permutation has two cycles. We use the recent result of Goulden, Nica, and Oancea on the number of maximal
Let $q$ be a prime power and $Vcong{mathbb F}_q^n$. A $t$-$(n,k,lambda)_q$ design, or simply a subspace design, is a pair ${mathcal D}=(V,{mathcal B})$, where ${mathcal B}$ is a subset of the set of all $k$-dimensional subspaces of $V$, with the prop
We introduce the random graph $mathcal{P}(n,q)$ which results from taking the union of two paths of length $ngeq 1$, where the vertices of one of the paths have been relabelled according to a Mallows permutation with real parameter $0<q(n)leq 1$. Thi
Recently, Bagno, Garber and Mansour studied a kind of excedance number on the complex reflection groups and computed its multidistribution with the number of fixed points on the set of involutions in these groups. In this note, we consider the simila
A detailed description of the structure of two-ended arc-transitive digraphs is given. It is also shown that several sets of conditions, involving such concepts as Property Z, local quasi-primitivity and prime out-valency, imply that an arc-transitiv