Parity Theorems for Statistics on Domino Arrangements
نویسندگان
چکیده
We study special values of Carlitz’s q-Fibonacci and q-Lucas polynomials Fn(q, t) and Ln(q, t). Brief algebraic and detailed combinatorial treatments are presented, the latter based on the fact that these polynomials are bivariate generating functions for a pair of statistics defined, respectively, on linear and circular domino arrangements.
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 ...
متن کاملA New Statistic on Linear and Circular r-Mino Arrangements
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.
متن کاملParity Theorems for Statistics on Lattice Paths and Laguerre Configurations
We examine the parity of some statistics on lattice paths and Laguerre configurations, giving both algebraic and combinatorial treatments. For the former, we evaluate q-generating functions at q = −1; for the latter, we define appropriate parity-changing involutions on the associated structures. In addition, we furnish combinatorial proofs for a couple of related recurrences.
متن کاملParity Theorems for Statistics on Permutations and Catalan Words
We establish parity theorems for statistics on the symmetric group Sn, the derangements Dn, and the Catalan words Cn, giving both algebraic and bijective proofs. For the former, we evaluate q-generating functions at q = −1; for the latter, we define appropriate signreversing involutions. Most of the statistics involve counting inversions or finding the major index of various words.
متن کاملOn some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 12 شماره
صفحات -
تاریخ انتشار 2005