Enumerating two permutation classes by the number of cycles
نویسندگان
چکیده
We enumerate permutations in the two permutation classes $\text{Av}_n(312, 4321)$ and $\text{Av}_n(321, 4123)$ by number of cycles each admits. also refine this enumeration with respect to several statistics.
منابع مشابه
Universal cycles for permutation classes
We define a universal cycle for a class of n-permutations as a cyclic word in which each element of the class occurs exactly once as an n-factor. We give a general result for cyclically closed classes, and then survey the situation when the class is defined as the avoidance class of a set of permutations of length 3, or of a set of permutations of mixed lengths 3 and 4. Résumé. Nous définissons...
متن کاملEnumerating permutation polynomials II: k-cycles with minimal degree
We consider the function m[k](q) that counts the number of cycle permutations of a finite field Fq of fixed length k such that their permutation polynomial has the smallest possible degree. We prove the upper–bound m[k](q) ≤ (k−1)!(q(q−1))/k for char(Fq) > e(k−3)/e and the lower–bound m[k](q) ≥ φ(k)(q(q−1))/k for q ≡ 1 (mod k). This is done by establishing a connection with the Fq–solutions of ...
متن کاملTwo Permutation Classes Enumerated by the Central Binomial Coefficients
We define a map between the set of permutations that avoid either the four patterns 3214, 3241, 4213, 4231 or 3124, 3142, 4123, 4132, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a bijection that allows us to determine some notable features of these permutations, such as the distribution of the statistics “number of ascents”, “number of l...
متن کاملEnumerating permutation polynomials
We consider the problem of enumerating polynomials over Fq, that have certain coefficients prescribed to given values and permute certain substructures of Fq. In particular, we are interested in the group of N -th roots of unity and in the submodules of Fq. We employ the techniques of Konyagin and Pappalardi to obtain results that are similar to their results in [Finite Fields and their Applica...
متن کاملEnumerating all Hamilton Cycles and Bounding the Number of Hamilton Cycles in 3-Regular Graphs
We describe an algorithm which enumerates all Hamilton cycles of a given 3regular n-vertex graph in time O(1.276n), improving on Eppstein’s previous bound. The resulting new upper bound of O(1.276n) for the maximum number of Hamilton cycles in 3-regular n-vertex graphs gets close to the best known lower bound of Ω(1.259n). Our method differs from Eppstein’s in that he considers in each step a n...
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 & Theoretical Computer Science
سال: 2022
ISSN: ['1365-8050', '1462-7264']
DOI: https://doi.org/10.46298/dmtcs.6173