Báo cáo toán học: "On the non-holonomic character of logarithms, powers, and the nth prime function" ppsx

... labelings ω and λ of P give rise to the same labeling of E(P )thenitiseasyto see that the set of (P, ω)-partitions and the set of (P, λ)-partitions are the same. In what follows we will often refer ... )=w p−r−1−i (P, ) for all i, and the symmetry follows. The relationship between the W -polynomials of (P, )and( P,µ) follows from Theorem 2.2 and the expans...

Ngày tải lên: 07/08/2014, 08:22

... give the to t al w-weight of all o f the members of L(n), the left-hand side by Theorem 5.1. As for the right-hand side, observe that the k-th term of the sum gives the total weight of all of the ... ···c, where the other elements of B are left undisturbed. Note that the ordering of B on the right has one more non-record low (the c) than the one of th...

Ngày tải lên: 08/08/2014, 14:23

... inverse of the function π(x) that gives the number of primes in the interval [1,x]. By the Prime Number Theorem, the function π(x)satisfies π(x) = Li(x)+R(x), where R(x) is of an order smaller than the ... Structure Theorem (as stated above in Theorem 2) and avoid some of the possible hardships due to the Stokes phenomenon.  Here is a direct application of Theore...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 05/08/2014, 10:20

... by w. The multiplication of A by  n i=1 1 1−t i and the extraction of the coefficient of t r 1 t r 2 ···t r n in the result corresponds at the set theoretic level to the concatenation of the signed ... used, these are sophisticated, and the problem serves as a useful study of these techniques, and the algebraic analysis gives partial information about the fo...

Ngày tải lên: 07/08/2014, 06:20

... values of the descendant sequence of 1. Golomb’s conjecture amounts to the assertion that, in the case B =1,foreachpositive integer k,thereisanunique way of assigning the value of b at these arguments, ... together with all of its descendants whose value under b is determined from the recursion (1) and the value of b at the seed. It seems reasonable that these sets...

Ngày tải lên: 07/08/2014, 06:20

... improve the text of the paper. This work was done during a long-term visit at the Mathemat- ical Institute of Cologne University. I thank the staff of the institute and personally P. Bundschuh for the ... (6) The case r = 1 of Problem 1 is trivial (that is why it is not included in the statement of the problem), while the cases r =2andr = 3 are treated in [6], [...

Ngày tải lên: 07/08/2014, 08:20

... respectively the set of successors of v ,the set of predecessors of v and the set of neighbors of v in G.Themaximum degree and minimum degree of a graph G are respectively denoted by ∆(G )and (G). We ... the proof of Theorem 2. 2 Definitions and notation In the rest of the paper, oriented graphs will be simply called graphs.ForagraphG and a vertex v of G,...

Ngày tải lên: 07/08/2014, 13:21

... describing the location of the roots of the generating polynomials of the numbers of derangements of length n, counted by their number of cycles. We then use this result to prove that if k is the number ... to the proof of Theorem 3.3. ✸ 4 Further Directions As we have mentioned, in the special case of q = 2, there are known combinatorial proofs for the balance...

Ngày tải lên: 07/08/2014, 13:21

... to modify Theorem 14 by using Theorem 9, similar to the proof of Theorem 12. The next theorem is a modification of [7, Theorem 4]. Theorem 15. K(tr, ts, ts; 2) ≤ t 2 K(r, s, s; 2). Proof. Let B ... until the total number of 1’s in the new matrix B is m. Since A is non-extendable, every element of R appears in the row and the column of an 0-entry in A. Thus for every 0-e...

Ngày tải lên: 07/08/2014, 15:22