Báo cáo toán học: "Chung-Feller Property in View of Generating Functions" pot

... (2011), #P104 5 Chung-Feller Property in View of Generating Functions Shu-Chung Liu ∗ Department of Applied Mathematics National Hsinchu University of Education Hsinchu City, Taiwan liularry@mail.nhcue.edu.tw Yi ... marked point is exactly the right end point of P , and then these m marked points cut P into m subpaths. Each of these subpaths contained a unique D d intersecti...

Ngày tải lên: 08/08/2014, 14:23

... conjectured a stronger form of one of their results. We give a simple inductive proof of this conjecture. Very recently, Regev and Zeilberger (Annals of Combinatorics, to appear) have inde- pendently proved ... the degrees of certain sequences of characters of the symmetric group, and note that they do not know a direct “finite” proof of their results. The purpose of the pres...

Ngày tải lên: 07/08/2014, 06:20

... determinants. In §2 the expansions of J ρ as determinants in e λ and m λ functions are given. The basic symmetry between these expansions is exhibited in §3, in which (7) is proved. The remaining ... journal of combinatorics 8 (2001), #R3 4 A similar development in m λ functions serves to corroborate the results in [3]. Combining the two results yields the following theorem, a...

Ngày tải lên: 07/08/2014, 06:22

... Λ(a) is an invariant of the Hurwitz action on Q n 2 m . In fact, it is easy to see that Λ(a) is invariant under each of the Hurwitz moves in (2.3) – (2.6). To determine the B n -orbits in Q n 2 m , ... for pointing out an error in Corol- lary 3.3 in a previous version of the paper. References [1] T. Ben-Itzhak and M. Teicher, Graph theoretic method for determining Hurwitz equi...

Ngày tải lên: 07/08/2014, 21:20

... Theorem 3.1, different n-tuples in (4.1) have different combinations of invariants λ(a) and π(a), while different n-tuples in (4.2) have different combinations of invariants λ(a), π(a), and u(a). ... p r ) is nonempty. Let J be the set of prime divisors of N that are not in I. By the Chinese Remainder Theorem, we can find an integer M satisfying the system of congruences M ≡ 0 (mod...

Ngày tải lên: 08/08/2014, 01:20

... for cubic graphs of large girth. Electron. J. Combin., 5 (1998) A1. [2] M. J. Hoare, On the girth of trivalent Cayley graphs. Graphs and Other Combinatorial Topics (Proceedings of the Third Czeckoslovak ... the smallest known trivalent graph of girth 14, improving the previous bound of 406 [2]. An electronic copy of the adjacency list is available at http://isu.indstate.edu/ge/CAG...

Ngày tải lên: 07/08/2014, 06:23

... in the same way as in the proof of Lemma 1. Lemma 3 Let λ be the number of distinct pairs of elements of B having the same cyclic ordering of edges incident on an element of A  . Then, if n ... ≤ cr D 5,z . Proof:Let h(t k ) be the sum of the number of crossings of the edges of t k with edges not incident on any vertex of T .Lett min be the element of T such that...

Ngày tải lên: 07/08/2014, 07:21

... proof to recent results by Dombi and by Chen and Wang concerning the number of representations of an integer in the form a 1 + a 2 , where a 1 and a 2 are elements of a given in nite set of integers. ... 1, ,n−1. This set, therefore, remains empty by the beginning of the nth step, and we initialize it inserting to it the smallest positive integer not contained in ∪ m l=1 A l ....

Ngày tải lên: 07/08/2014, 08:22

... 2. (∗) The rest of the argument splits into cases depending on the number of tags appearing in P . If P = w · w does not contain any tag then it must be entirely contained in one of: 201, α a , ... to all digits in γ i−1 . The first few strings γ i are listed in Table 1. By counting the number of 1’s between consecutive 0’s in γ i we obtain consecutive digits of a new strin...

Ngày tải lên: 07/08/2014, 21:21

... tudy of minimally intersecting set partitions, we investi- gate minimally intersecting set partitions of type B. Our main result is a formula for the number of m inimally intersecting r-tuples of ... number of ways to assign 0 or 1 to all kl pairwise intersections of blocks of two minimally intersecting ordinary partitions. We will use a similar idea to deal with the intersectin...

Ngày tải lên: 08/08/2014, 11:20