arXiv subjects

Brooke Orosz

Publications and source records attributed to Brooke Orosz.

3 recordsLinked to original sources

arXiv2008

Explicit constructions of infinite families of MSTD sets

We explicitly construct infinite families of MSTD (more sums than differences) sets. There are enough of these sets to prove that there exists a constant C such that at least C / r^4 of the 2^r subsets of {1,...,r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2^{r/2} for some polynomial f(r)). We conclude by generalizing our method to compare linear forms epsilon_1 A + ... + epsilon_n A with epsilon_i in {-1,1}.

math.NT↗

arXiv2007

Asymptotic estimates for phi functions for subsets of {m+1, m+2,...,n}

Let f(m,n) denote the number of relatively prime subsets of {m+1,m+2,...,n}, and let Phi(m,n) denote the number of subsets A of {m+1,m+2,...,n} such that gcd(A) is relatively prime to n. Let f_k(m,n) and Phi_k(m,n) be the analogous counting functions restricted to sets of cardinality k. Simple explicit formulas and asymptotic estimates are obtained for these four functions.

math.NT↗

arXiv2007

Binary linear forms over finite sets of integers

Let A be a finite set of integers. For a polynomial f(x_1,...,x_n) with integer coefficients, let f(A) = {f(a_1,...,a_n) : a_1,...,a_n \in A}. In this paper it is proved that for every pair of normalized binary linear forms f(x,y)=u_1x+v_1y and g(x,y)=u_2x+v_2y with integral coefficients, there exist arbitrarily large finite sets of integers A and B such that |f(A)| > |g(A)| and |f(B)| < |g(B)|.

math.NT↗