Minnesota Journal of Undergraduate Mathematics https://pubs.lib.umn.edu/index.php/mjum <p>The Minnesota Journal of Undergraduate Mathematics focuses on original mathematical research, done primarily by undergraduates, in all areas of mathematics and its applications. The journal is currently not accepting new articles, while we work to process all of the current submissions. Authors with submissions should watch for updates via email. We anticipate accepting new submissions later in 2024. </p> <p><strong>Sponsors</strong><br /><a href="https://math.umn.edu/" target="_new">School of Mathematics</a><br /><a href="http://www.mathcep.umn.edu/" target="_new">Math Center for Educational Programs (MathCEP)</a><br /><a href="https://www.ima.umn.edu/" target="_new">Institute for Mathematics and its Applications</a></p> en-US mjum@umn.edu (MJUM Editorial Team) mjum@umn.edu (MJUM Editorial Team) Mon, 19 Feb 2024 23:21:57 -0600 OJS 3.3.0.7 http://blogs.law.harvard.edu/tech/rss 60 Expected Value of Statistics on Type-B Permutation Tableaux https://pubs.lib.umn.edu/index.php/mjum/article/view/4174 <p>Type-B permutation tableaux are combinatorial objects introduced by Lam and Williams that have an interesting connection with the partially asymmetric simple exclusion process (PASEP). In this paper, we compute the expected value of several statistics on these tableaux. Some of these computations are motivated by a similar paper on permutation tableaux. Others are motivated by the PASEP. In particular, we compute the expected number of rows, unrestricted rows, diagonal ones, adjacent south steps, and adjacent west steps.</p> Ryan Althoff, Daniel Diethrich, Amanda Lohss, Xin-Dee Low, Emily Wichert Copyright (c) 2024 Minnesota Journal of Undergraduate Mathematics https://pubs.lib.umn.edu/index.php/mjum/article/view/4174 Mon, 19 Feb 2024 00:00:00 -0600 The Legendre Approximation and Arithmetic Bias https://pubs.lib.umn.edu/index.php/mjum/article/view/4998 <p>An interesting episode in the history of the prime number theorem concerns a formula proposed by Legendre for counting the primes below a given bound. We point out that arithmetic bias likely played an important role in arriving at that formula and in its subsequent widespread, decades-long recognition. We also show that the Legendre constant 1.08366 satisfies a certain simple and natural criterion, and conjecture that this criterion is how Legendre arrived at that erroneous constant in his formula.</p> Megan Paasche, Ghaith Hiary Copyright (c) 2024 Minnesota Journal of Undergraduate Mathematics https://pubs.lib.umn.edu/index.php/mjum/article/view/4998 Mon, 19 Feb 2024 00:00:00 -0600 Some Thoughts on the Search for 5 × 5 and 6 × 6 Additive-Multiplicative Magic Squares https://pubs.lib.umn.edu/index.php/mjum/article/view/6015 <div class="page" title="Page 2"> <div class="layoutArea"> <div class="column"> <p>An <em>additive-multiplicative</em> magic square is a square grid of numbers whose rows, columns, and long diagonals all have the same sum (called the magic sum) and the same product (called the magic product). There are numerous open problems about magic squares by Christian Boyer on <a href="multimagie.com">multimagie.com</a>. One such problem is to construct or prove the impossibility of a 5 × 5 or 6 × 6 additive-multiplicative magic square of distinct positive integers. Here, we present a possible approach to this problem and some partial results. We observe that such a square can be described by a form determined by the prime factor- izations of its entries and that identifying these forms might be helpful in finding such a square or ruling out specific magic products.</p> </div> </div> </div> Desmond Weisenberg Copyright (c) 2024 https://pubs.lib.umn.edu/index.php/mjum/article/view/6015 Mon, 19 Feb 2024 00:00:00 -0600