The generation of k-designs (pseudorandom distributions that emulate the Haar measure up
to k moments) with local quantum circuit ensembles is a problem of fundamental importance …

Elements of high order in finite fields of the form Fq[x]/Φr(x) Page 1 Finite Fields and Their
Applications 18 (2012) 700–710 Contents lists available at SciVerse ScienceDirect Finite Fields …

Let p be a prime and let G be a finite group. A complex character of G is called almost p-
rational if its values belong to a cyclotomic field ℚ⁢(e 2⁢ π⁢ i/n) for some n∈ ℤ+ not …

Finite primitive groups of small rank have been studied for a long time because they are a
natural source of important examples and because of their applications to various parts of …

We prove that for every ϵ> 0 there exists a δ> 0 such that every group of order n≥ 3 has at
least δ⁢ log 2⁡ n/(log 2⁡ log 2⁡ n) 3+ ϵ conjugacy classes. This sharpens earlier results of …

We study separations between two fundamental models (or\emph {Ans\" atze}) of
antisymmetric functions, that is, functions $ f $ of the form $ f (x_ {\sigma (1)},\ldots, x …

In 2003, Maróti showed that one could use the machinery of ℓ-cores and ℓ-quotients of
partitions to establish lower bounds for p (n), the number of partitions of n. In this paper we …

The efficiency of locally generating unitary designs, which capture statistical notions of
quantum pseudorandomness, lies at the heart of wide-ranging areas in physics and …

Some observations concerning the lattices of integer partitions are presented. We determine
the size of the standard contexts, discuss a recursive construction and show that the lattices …

For a finite group G, let k (G) denote the number of conjugacy classes of G. If G is a finite
permutation group of degree n> 2, then k (G)≤ 3 (n− 1)/2. This is an extension of a theorem …