I am applying for pure Math Ph.D programs this year.
I did some independent research in centralizer of matrices, and I developed an algorithm to generate the explicit k-basis for the space of centralizers. I guess this problem is not solved since I cannot find any papers on this topic, and a similar question asked on Math Stack Overflow has no complete solutions.
I asked my professor (one of my recommendation letter writer) to take a look, but this is irrelevant to his fields of studies and he said that he might have no time to read this.
I want this research experience to strengthen my application. So, how should I deal with my paper? Shall I just mention it in my resume and personal statement or should I post the paper on arXiv? I am not sure what is appropriate.