Báo cáo toán học: "On a Multiplicative Partition Function" pps

... York-London- Sydney, 1974. [6] A. Oppenheim, On an arithmetic function, J. London Math. Soc. 1 (1926), 205- 211. [7] M. V. Subbarao and A. Verma, Some remarks on a product expansion: an unex- plored partition function, ... reading of the manuscript and for correcting a crucial mistake in the proof of Theorem 2. References [1] P.T.Bateman,Privatecommunication. [2] D. Bowman, Private co...

Ngày tải lên: 07/08/2014, 06:22

... obtain a combinatorial interpretation for Stanley’s partition function t(n), which can be recast as a combinatorial interpretation for u(n). Theorem 3.2 The partition function t(n) is equal to ... similar t o Andrews’ proof of (1.3) for t(n). As a consequence, one sees that t(n) and p(n) have the same parity for any nonnegative integer n. This fact also has a simple combinatorial...

Ngày tải lên: 08/08/2014, 11:20

... The Main Theorem We begin with some preliminaries about partitions and their conjugates. For a given partition π with parts each  N,wedenotebyf i (π) the number of appearances of i as a part ... following be dealing with partitions whose parts are all  some given N.Welet¯π be that partition made up of the parts of π that are <N. In light of (11) we see that if N is a part of π...

Ngày tải lên: 07/08/2014, 08:22

... C. Evans, Partial Diff. Equations, American Math. Society, 1998. 5. C. Vargas an d M. Zuluaga, On a Nonlinear Dirichlet Problem Type at Resonance and Bifurcation, Partial Differential Equations, ... Elliptic Equations on an Unbounded Domain Hoang Quoc Toan Fa culty of Math., Mech. and Inform. Vietnam National University, 334 Nguyen Trai, Hanoi, Vietnam Received Ma y 12, 2004 Revised August 28...

Ngày tải lên: 06/08/2014, 05:20

... spaces of random variables, Math. Uspekhi 101 (1976) 417–454 (Russian). 28. V.M. Zolotarev, Ideal metrics in the problems of probability theory and mathe- matical statistics, Austral. J. Statist. ... the approximating type a metric as a comparison measure must be selected in accordance with the requirements to its properties. In recent years several results of applied mathematics and info...

Ngày tải lên: 06/08/2014, 05:20

... t)]   and we already know that the absolute value of the inner sum was found to be smaller than 3 √ q/2. One may extend the codes C(q, n) in a similar way. Using the same approach as that in ... follows that the polynomial P (X)=(X + x)(X + x)(X + y)(X + y) On a Class of Constant Weight Codes Mihai Caragiu Institute of Mathematics Bucharest and Department of Mathematics, Pennsylvania St...

Ngày tải lên: 07/08/2014, 06:20

... these are sophisticated, and the problem serves as a useful study of these techniques, and the algebraic analysis gives partial information about the formulation of a bijective proof. The paper ... signs multiplicatively and erase the subscripts on w to get a signed divided string on n available symbols because there are nS x ’s, such that every t i appears no more than r times (since w...

Ngày tải lên: 07/08/2014, 06:20

... Department of Mathematics University of Toronto University of Toronto Toronto, Canada M5S 1A1 Toronto, Canada M5S 1A1 barbeau@math.utoronto.ca tanny@math.utoronto.ca Submitted: January 4, 1996; Accepted: ... metafibonacci type, parameterized by k,and,foreachk, identified what he speculated was the unique increas- ing solution. We show that, to the contrary, there are many increasing solutions...

Ngày tải lên: 07/08/2014, 06:20

... totally dyadic representation A. A dyadic oriented matriod is dyadic of order k if it has a totally dyadic representation A with full row rank and with the property that for each pair of adjacent ... Louisville. scobee@louisville.edu Submitted: January 7, 1999; Accepted: March 30, 1999 Abstract A rational matrix is totally dyadic if all of its nonzero subdeterminants are in {±2 k : k...

Ngày tải lên: 07/08/2014, 06:20

... Kostochka ∗ University of Illinois at Urbana–Champaign, Urbana, IL 61801 and Institute of Mathematics, Novosibirsk 630090, Russia kostochk@math.uiuc.edu Submitted: April 10, 2002; Accepted: August ... exp{c 2 r/k}. Note that the lower bound on p(r, k)withc 1 =1/4 follows also from Theorem 3 of the seminal paper [5] by Erd˝os and Lov´asz. We say that a k-uniform hypergraph G is k-partite,ifV...

Ngày tải lên: 07/08/2014, 06:23