A New Statistic on Linear and Circular r-Mino Arrangements
نویسندگان
چکیده
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.
منابع مشابه
Periodicity and Parity Theorems for a Statistic on r-Mino Arrangements
If r > 2, the r-Fibonacci numbers F (r) n are defined by F (r) 0 = F (r) 1 = · · · = F (r) r−1 = 1, with F (r) n = F (r) n−1 + F (r) n−r if n > r. The r-Lucas numbers L (r) n are defined by L (r) 1 = L (r) 2 = · · · = L (r) r−1 = 1 and L (r) r = r + 1, with L (r) n = L (r) n−1 + L (r) n−r if n > r + 1. If r = 2, the F (r) n and L (r) n reduce, respectively, to the classical Fibonacci and Lucas ...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 13 شماره
صفحات -
تاریخ انتشار 2006