Enumeration of Restricted Permutation Triples
نویسندگان
چکیده
Let [n] stand for the first n natural numbers {1, 2, · · · , n} and Sn for the permutations of [n]. Given a permutation π = (a1, a2, · · · , an) ∈ Sn, a rise (shortly as “R”) at the kth position refers to ak < ak+1, while a fall (shortly as “F”) at the same position refers to ak > ak+1, where the position index k runs from 1 to n − 1. It is classically well–known (cf. Comtet [2, §6.5]) that the number of the permutations of [n] with exactly k − 1 rises is equal to the Eulerian number A(n, k), which admits the following bivariate generating function 1 + ∑
منابع مشابه
Enumeration Schemes for Restricted Permutations
Zeilberger’s enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WilfPlus, which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decomposi...
متن کاملO ct 2 00 6 RESTRICTED MOTZKIN PERMUTATIONS , MOTZKIN PATHS , CONTINUED FRACTIONS , AND CHEBYSHEV POLYNOMIALS
We say that a permutation π is a Motzkin permutation if it avoids 132 and there do not exist a < b such that π a < π b < π b+1. We study the distribution of several statistics in Motzkin permutations, including the length of the longest increasing and decreasing subsequences and the number of rises and descents. We also enumerate Motzkin permutations with additional restrictions, and study the ...
متن کاملType-Itemized Enumeration of RS-Stereoisomers of Octahedral Complexes
Stereoisograms of octahedral complexes are classified into five types (type I--typeV) under the action of the corresponding RS-stereoisomeric group. Their enumeration is accomplished in a type-itemized fashion, where Fujita's proligand method developed originally for combinatorial enumeration under point groups (S. Fujita, Theor. Chem. Acc., 113, 73--79 (2005)) is extended to meet the requireme...
متن کاملRestricted Dumont permutations, Dyck paths, and noncrossing partitions
We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that use...
متن کاملEnumeration Schemes for Words Avoiding Permutations
The enumeration of permutation classes has been accomplished with a variety of techniques. One wide-reaching method is that of enumeration schemes, introduced by Zeilberger and extended by Vatter. In this paper we further extend the method of enumeration schemes to words avoiding permutation patterns. The process of finding enumeration schemes is programmable and allows for the automatic enumer...
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 17 شماره
صفحات -
تاریخ انتشار 2010