Greg Dresden

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math.CO2026

Self-Convolutions of Generalized Narayana Numbers

Greg Dresden, Yuechen Xiao, Guanzhang Zhou

For the Fibonacci numbers $F_{n}$ , we have the self-convolution formula $5 \sum_{i = 0}^{n} F_{i} F_{n - i} = (2 n) F_{n + 1} - (n + 1) F_{n}$ . We find the corresponding self-convolution formula for…

math.CO2024

Areas Between Cosines

Muhammad Adam Dombrowski, Gregory Dresden

We find the area between $cos^{p} x$ and $cos^{p} n x$ as $n$ heads to infinity, and we establish a connection between these limiting values and the exponential generating function fo…

math.CO2024

Look, There's More to Say about Conway's Look and Say Sequence

Greg Dresden, Jacob Siehler

We take Conway's Look and Say Sequence into a base-3 world, and we discover that there are only 24 interesting and irreducible sequences in base 3.