Michael Allen

activity

20192022

most citedConnections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices

4 citations · 9 across the 9 of their papers we have counts for

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Showing 2022 · math.COShow all

4 papers · 2 filters

math.CO2022

Combinations without specified separations

Michael A. Allen

We consider the restricted subsets of $N_{n} = {1, 2, \dots, n}$ with $q \geq 1$ being the largest member of the set $Q$ of disallowed differences between subset eleme…

math.CO2022★ 1 cited

On a Two-Parameter Family of Generalizations of Pascal's Triangle

Michael A. Allen

We consider a two-parameter family of triangles whose $(n, k)$ -th entry (counting the initial entry as the $(0, 0)$ -th entry) is the number of tilings of $N$ -boards (which are linear…

math.CO2022★ 1 cited

On Two Families of Generalizations of Pascal's Triangle

Michael A. Allen, Kenneth Edwards

We consider two families of Pascal-like triangles that have all ones on the left side and ones separated by $m - 1$ zeros on the right side. The $m = 1$ cases are Pascal's triangle and…

math.CO2022

Identities involving the tribonacci numbers squared via tiling with combs

Michael A. Allen, Kenneth Edwards

The number of ways to tile an $n$ -board (an $n \times 1$ rectangular board) with $(\frac{1}{2}, \frac{1}{2}; 1)$ -, $(\frac{1}{2}, \frac{1}{2}; 2)$ -, and $(\frac{1}{2}, \frac{1}{2}; 3)$ -combs is $T_{n + 2}^{2}$ where…