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- W1989974360 abstract "In this paper we will explore two seemingly unrelated counting questions, both of which are answered by the same formula. In the first section, we find the surface areas of certain solids formed from unit cubes. In second section, we enumerate permutations with a specified set of restrictions. Next, we give a bijection between the faces of the solids and the set of permutations. We conclude with suggestions for further reading. First, however, it is worth explaining how this paper came about. The author received an email from David Harris while he was helping his 12-year-old daughter complete a project for her math class. Together Harris and his daughter constructed triangular piles of cubes. After creating an increasing sequence of these piles, they computed the surface area of each pile, and hoped to find a formula for the surface area of their nth pile. This project and its solution are described in the next section. At the time of their correspondence, Harris and his daughter had deduced several facts about the construction but were unable to find a formula for the surface area in general. When they searched for the first few terms in their sequence, Google returned only one hit: a Maple data file on the author’s website. The sequence that Harris and his daughter discovered online was originally generated in the context of pattern-avoiding words and permutations. Their web search produced a conjecture that gives a nice geometric interpretation of a permutation patterns question. This serendipitous discovery of the surprising and beautiful connection between a geometry problem and an enumeration problem illustrates how attractive new results may sometimes appear in such a surprising place as an elementary homework exercise." @default.
- W1989974360 created "2016-06-24" @default.
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- W1989974360 date "2010-10-01" @default.
- W1989974360 modified "2023-09-24" @default.
- W1989974360 title "Stacking Blocks and Counting Permutations" @default.
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- W1989974360 doi "https://doi.org/10.4169/002557010x521868" @default.
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