Transitive cycle factorizations and prime parking functions
نویسندگان
چکیده
Minimal transitive cycle factorizations and parking functions are related very closely. Using the correspondence between them, we find a bijection between minimal transitive factorizations of permutations of type (1, n − 1) and prime parking functions of length n.
منابع مشابه
Refined Enumeration of Minimal Transitive Factorizations of Permutations
Minimal transitive cycle factorizations, parking functions and labeled trees are related very closely. Using the correspondences between them, we find a refined enumeration of minimal transitive factorizations of permutations of type (1, n− 1) and (2, n− 2).
متن کاملTwo-geodesic transitive graphs of prime power order
In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...
متن کاملProduct of normal edge-transitive Cayley graphs
For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.
متن کاملOn transitive one-factorizations of arc-transitive graphs
An equivalent relation between transitive 1-factorizations of arctransitive graphs and factorizations of their automorphism groups is established. This relation provides a method for constructing and characterizing transitive 1-factorizations for certain classes of arc-transitive graphs. Then a characterization is given of 2-arc-transitive graphs which have transitive 1factorizations. In this c...
متن کاملCombinatorial Constructions for Transitive Factorizations in the Symmetric Group
We consider the problem of counting transitive factorizations of permutations; that is, we study tuples (σr , . . . , σ1) of permutations on {1, . . . , n} such that (1) the product σr · · · σ1 is equal to a given target permutation π , and (2) the group generated by the factors σi acts transitively on {1, . . . , n}. This problem is widely known as the Hurwitz Enumeration Problem, since an enc...
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:
- J. Comb. Theory, Ser. A
دوره 104 شماره
صفحات -
تاریخ انتشار 2003