A New Statistic on Linear and Circular $r$-Mino Arrangements

Mark A. Shattuck, Carl G. Wagner


We introduce a new statistic on linear and circular $r$-mino arrangements which leads to interesting polynomial generalizations of the $r$-Fibonacci and $r$-Lucas sequences. By studying special values of these polynomials, we derive periodicity and parity theorems for this statistic.

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