Baxter Permutations, Maj-balances, and Positive Braids

نویسندگان

  • Sen-Peng Eu
  • Tung-Shan Fu
  • Yeh-Jong Pan
  • Chien-Tai Ting
چکیده

In this paper we present two interesting properties of 321-avoiding Baxter permutations. The first one is a variant of refined major-balance identity for the 321avoiding Baxter permutations, respecting the number of fixed points and descents. The second one is a bijection between the 321-avoiding Baxter permutations with the entry 1 preceding the entry 2 and the positive braid words on four strands.

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

On Counting Permutations by Pairs of Congruence Classes of Major Index

For a fixed positive integer n, let Sn denote the symmetric group of n! permutations on n symbols, and let maj(σ) denote the major index of a permutation σ. Fix positive integers k < l ≤ n, and nonnegative integers i, j. Let mn(i\k; j\l) denote the cardinality of the set {σ ∈ Sn : maj(σ) ≡ i mod k,maj(σ) ≡ j mod l}. In this paper we give some enumerative formulas for these numbers. When l divid...

متن کامل

A new derivation of the generating function for the major index

Consider the sequence w = w1w2 . . . w, where wi E [w, 1 =Z i c n. The Descent Set of w, D(w) is {i ) 1 s i Wi+l}y and the major index, Maj(w) is the sum of all the elements (possibly zero) of D(w). MacMahon [4,5] showed that the major indices of the set of all permutations of w has the same generating function as the inversion numbers, Inv(w) of these permutations. A combinatorial proo...

متن کامل

Sub-families of Baxter Permutations Based on Pattern Avoidance

Baxter permutations are a class of permutations which are in bijection with a class of floorplans that arise in chip design called mosaic floorplans. We study a subclass of mosaic floorplans called Hierarchical Floorplans of Order k defined from mosaic floorplans by placing certain geometric restrictions. This naturally leads to studying a subclass of Baxter permutations. This subclass of Baxte...

متن کامل

The Expected Shape of Random Doubly Alternating Baxter Permutations

Guibert and Linusson introduced the family of doubly alternating Baxter permutations, i.e. Baxter permutations æ 2 Sn , such that æ and æ°1 are alternating. They proved that the number of such permutations in S2n and S2n+1 is the Catalan number Cn . In this paper we compute the expected limit shape of such permutations, following the approach by Miner and Pak.

متن کامل

Bijective Counting of Involutive Baxter Permutations

We enumerate bijectively the family of involutive Baxter permutations according to various parameters; in particular we obtain an elementary proof that the number of involutive Baxter permutations of size 2n with no fixed points is 3·2 n−1

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 19  شماره 

صفحات  -

تاریخ انتشار 2012