From the 1 of 13 linked papers with an AI index.
13 papers
The Godsil--McKay Asymptotic for Latin Rectangles in the Sublinear Range of ErdÅs Problem 725
Eric Li
ErdÅs Problem 725 asks for an asymptotic formula for the number of ordered, labelled Latin rectangles. Godsil and McKay proved that $L_{k,n}\sim (n!)^k((n)_k…
A Resolution of ErdÅs Problem 768: the Sylow Divisor Condition
Eric Li
The paper solves Erdős Problem 768 by determining the exact leading constant in the asymptotic formula for the proportion of integers whose every prime divisor has a co‑divisor con…
A Resolution of ErdÅs Problem 731 under Dyadic Regularity
Eric Li
We resolve ErdÅs Problem 731 under the explicit dyadic-regularity formalization of "reasonable." Let be the least positive integer not dividing . On dyadic i…
A resolution of ErdÅs Problem 1061 on the sum-of-divisors function
Eric Li
We resolve ErdÅs Problem 1061, the question whether the number \[ S(x)=\#\{(a,b)\in\mathbb{N}^2:a+b\le x, \ Ï(a)+Ï(b)=Ï(a+b)\} \] of ordered solutions has a linear asymptotic $…
A Resolution of ErdÅs Problems 593 and 1177: Obligatory Triple Systems and Exact Spectra
Eric Li
We resolve ErdÅs Problems #593 and #1177. Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system; the answer is exactly the class generat…
Prime-Power Rarefaction and a Density-One Lower Bound for ErdÅs Problem 400
Eric Li
For fixed , let be the greatest excess among positive integers satisfying . We prove that, for every $\varepsilon>…