A morphic approach to combinatorial games: the Tribonacci case

نویسندگان

  • Éric Duchêne
  • Michel Rigo
چکیده

We propose a variation of Wythoff’s game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cubic Pisot unit combinatorial games

Generalized Tribonacci morphisms are defined on a three letters alphabet and generate the so-called generalized Tribonacci words. We present a family of combinatorial removal games on three piles of tokens whose set of P-positions is coded exactly by these generalized Tribonacci words. To obtain this result, we study combinatorial properties of these words like gaps between consecutive identica...

متن کامل

A Generalization of the $k$-Bonacci Sequence from Riordan Arrays

In this article, we introduce a family of weighted lattice paths, whose step set is {H = (1, 0), V = (0, 1), D1 = (1, 1), . . . , Dm−1 = (1,m − 1)}. Using these lattice paths, we define a family of Riordan arrays whose sum on the rising diagonal is the k-bonacci sequence. This construction generalizes the Pascal and Delannoy Riordan arrays, whose sum on the rising diagonal is the Fibonacci and ...

متن کامل

A Pascal-like Triangle Related to the Tribonacci Numbers

A tile composed of two pieces, which we refer to as a fence tile, is introduced to give the Tribonacci numbers a new combinatorial interpretation. The interpretation is used to construct a Pascal-like triangle and various identities concerning the triangle are proven. An intuitive proof of a general identity for the Tribonacci numbers in terms of sums of products of the binomial coefficients is...

متن کامل

A Deterministic Multiple Key Space Scheme for Wireless Sensor Networks via Combinatorial Designs

The establishing of a pairwise key between two nodes for encryption in a wireless sensor network is a challenging issue. To do this, we propose a new deterministic key pre-distribution scheme which has modified the multiple key space scheme (MKSS). In the MKSS, the authors define two random parameters to make better resilience than existing schemes. Instead of a random selection of these parame...

متن کامل

On Tribonacci Sequences

The aim of this note is to give a simple construction of the Tribonacci sequences, namely they consist of the occurrences of letters in an infinite word obtained as the fixed point of the morphism θ defined by θ : a → ab; b → ac; c → a. The construction is combinatorial and admits a generalization to k-bonacci sequences.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • ITA

دوره 42  شماره 

صفحات  -

تاریخ انتشار 2008