Sharp sets of permutations
نویسندگان
چکیده
منابع مشابه
Sharply $(n-2)$-transitive Sets of Permutations
Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...
متن کاملDescent sets of cyclic permutations
We present a bijection between cyclic permutations of {1, 2, . . . , n+1} and permutations of {1, 2, . . . , n} that preserves the descent set of the first n entries and the set of weak excedances. This non-trivial bijection involves a Foata-like transformation on the cyclic notation of the permutation, followed by certain conjugations. We also give an alternate derivation of the consequent res...
متن کاملRegular closed sets of permutations
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets to be enumerated by rational generating functions. As a consequence we give the first non-trivial examples of pattern closed sets of permutations all of whose closed subclasses ha...
متن کاملVC-Dimension of Sets of Permutations
We deene the VC-dimension of a set of permutations A S n to be the maximal k such that there exist distinct i 1 ; :::; i k 2 f1; :::; ng that appear in A in all possible linear orders, that is, every linear order of fi 1 ; :::; i k g is equivalent to the standard order of f(i 1); :::; (i k)g for at least one permutation 2 A. In other words, the VC-dimension of A is the maximal k such that for s...
متن کاملCompositions of pattern restricted sets of permutations
The composition of two pattern restricted classes X,Y is the set of all permutation products θφ where θ ∈ X,φ ∈ Y . This set is also defined by pattern restrictions. Examples are given where this set of restrictions is finite and where it is infinite. The composition operation is studied in terms of machines that sort and generate permutations. The theory is then applied to a multistage sorting...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90252-3