Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials

نویسندگان

  • Eric S. Egge
  • Toufik Mansour
چکیده

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243 and 2143. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid 1243, 2143, and certain additional patterns. We also give generating functions for permutations which avoid 1243 and 2143 and contain certain additional patterns exactly once. In all cases we express these generating functions in terms of Chebyshev polynomials of the second kind.

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

A ug 2 00 2 Permutations Which Avoid 1243 and 2143 , Continued Fractions , and Chebyshev Polynomials ∗

Several authors have examined connections between permutations which avoid 132, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of some of these results for permutations which avoid 1243 and 2143. Using tools developed to prove these analogues, we give enumerations and generating functions for permutations which avoid 1243, 2143, and certain a...

متن کامل

Horse paths, restricted 132-avoiding permutations, continued fractions, and Chebyshev polynomials

Several authors have examined connections among 132-avoiding permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we find analogues for some of these results for permutations π avoiding 132 and 1223 (there is no occurrence πi < πj < πj+1 such that 1 ≤ i ≤ j − 2) and provide a combinatorial interpretation for such permutations in terms of lattice paths. ...

متن کامل

ul 2 00 3 Restricted 3412 - Avoiding Involutions : Continued Fractions , Chebyshev Polynomials and Enumerations ∗

Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to gi...

متن کامل

RESTRICTED 132-AVOIDING k-ARY WORDS, CHEBYSHEV POLYNOMIALS, AND CONTINUED FRACTIONS

We study generating functions for the number of n-long k-ary words that avoid both 132 and an arbitrary `-ary pattern. In several interesting cases the generating function depends only on ` and is expressed via Chebyshev polynomials of the second kind and continued fractions. 1. Extended abstract 1.1. Permutations. Let Sn denote the set of permutations of [n] = {1, 2, . . . , n}, written in one...

متن کامل

On the Diagram of Schröder Permutations

Egge and Mansour have recently studied permutations which avoid 1243 and 2143 regarding the occurrence of certain additional patterns. Some of the open questions related to their work can easily be answered by using permutation diagrams. As for 132-avoiding permutations the diagram approach gives insights into the structure of {1243, 2143}-avoiding permutations that yield simple proofs for some...

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:
  • Electr. J. Comb.

دوره on  شماره 

صفحات  -

تاریخ انتشار 2002