A non-trivial intersection theorem for permutations with fixed number of cycles
نویسندگان
چکیده
منابع مشابه
Gray code for permutations with a fixed number of cycles
We give the first Gray code for the set of n-length permutations with a given number of cycles. In this code, each permutation is transformed into its successor by a product with a cycle of length three, which is optimal. If we represent each permutation by its transposition array then the obtained list still remains a Gray code and this allows us to construct a constant amortized time (CAT) al...
متن کاملAn Erdős-Ko-Rado Theorem for Permutations with Fixed Number of Cycles
Let Sn denote the set of permutations of [n] = {1, 2, . . . , n}. For a positive integer k, define Sn,k to be the set of all permutations of [n] with exactly k disjoint cycles, i.e., Sn,k = {π ∈ Sn : π = c1c2 · · · ck}, where c1, c2, . . . , ck are disjoint cycles. The size of Sn,k is [ n k ] = (−1)n−ks(n, k), where s(n, k) is the Stirling number of the first kind. A family A ⊆ Sn,k is said to ...
متن کاملPermutations with extremal number of fixed points
Abstract. We extend Stanley’s work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting permutations we study their generating polynomials by number of excedances. Several techniques are used: Désarménien’s desarrangement combinatorics, Ge...
متن کاملIndecomposable permutations with a given number of cycles
A permutation a1a2 . . . an is indecomposable if there does not exist p < n such that a1a2 . . . ap is a permutation of {1, 2, . . . , p}. We compute the asymptotic probability that a permutation of Sn with m cycles is indecomposable as n goes to infinity with m/n fixed. The error term is O( log(n−m) n−m ). The asymptotic probability is monotone in m/n, and there is no threshold phenomenon: it ...
متن کاملExtension of Krull's intersection theorem for fuzzy module
In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic comp...
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: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.09.032