From ejc-list-admin@cs.anu.edu.au Mon Aug 23 19:27:23 2004 Received: from euclid.math.temple.edu (euclid.math.temple.edu [155.247.28.2]) by math.rutgers.edu (8.11.7p1+Sun/8.8.8) with ESMTP id i7NNRMQ21102 for ; Mon, 23 Aug 2004 19:27:22 -0400 (EDT) Received: by euclid.math.temple.edu (Postfix) id A8AA539243; Mon, 23 Aug 2004 19:27:22 -0400 (EDT) Delivered-To: zeilberg@euclid.math.temple.edu Received: from localhost (localhost [127.0.0.1]) by euclid.math.temple.edu (Postfix) with ESMTP id 987F7392FF for ; Mon, 23 Aug 2004 19:27:22 -0400 (EDT) Received: from cs.anu.edu.au (cs.anu.edu.au [150.203.164.35]) by euclid.math.temple.edu (Postfix) with ESMTP id AD4A5392F7 for ; Mon, 23 Aug 2004 19:27:20 -0400 (EDT) Received: from localhost ([127.0.0.1] helo=cs.anu.edu.au ident=list) by cs.anu.edu.au with esmtp (Exim 3.35 #1 (Debian)) id 1BzNlj-0005so-00; Tue, 24 Aug 2004 08:58:27 +1000 Received: from hans.math.upenn.edu ([130.91.49.156]) by cs.anu.edu.au with esmtp (Exim 3.35 #1 (Debian)) id 1BzNiD-0005sW-00 for ; Tue, 24 Aug 2004 08:54:49 +1000 Received: (from eljc@localhost) by hans.math.upenn.edu (8.11.0P2/8.11.0) id i7NMsk802708 for EJC-list@cs.anu.edu.au; Mon, 23 Aug 2004 18:54:46 -0400 (EDT) Date: Mon, 23 Aug 2004 18:54:46 -0400 From: E-JC To: EJC-list@cs.anu.edu.au Message-ID: <20040823225446.GA2706@hans.math.upenn.edu> Reply-To: please do not reply to this mail Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline User-Agent: Mutt/1.4.2i Subject: [E-JC] From the Electronic Journal of Combinatorics Sender: ejc-list-admin@cs.anu.edu.au Errors-To: ejc-list-admin@cs.anu.edu.au X-BeenThere: ejc-list@cs.anu.edu.au X-Mailman-Version: 2.0.11 Precedence: bulk List-Help: List-Post: List-Subscribe: , List-Id: Electronic Journal of Combinatorics announcements List-Unsubscribe: , X-Virus-Scanned: by AMaViS snapshot-20020531 Status: R Content-Length: 2495 The following 3 papers have been published in The Electronic Journal of Combinatorics. They can be viewed at . Click on the button or link for Volume 11 (1). ============================== R53. Mohamud Mohammed and Doron Zeilberger: The Markov-WZ Method Publication date: Aug 23, 2004 Abstract: Andrei Markov's 1890 method for convergence-acceleration of series bears an amazing resemblance to WZ theory, as was recently pointed out by M. Kondratieva and S. Sadov. But Markov did not have Gosper and Zeilberger's algorithms, and even if he did, he wouldn't have had a computer to run them on. Nevertheless, his beautiful ad-hoc method, when coupled with WZ theory and Gosper's algorithm, leads to a new class of identities and very fast convergence-acceleration formulas that can be applied to any infinite series of hypergeometric type. ============================== R54. Robert A. Sulanke: Generalizing Narayana and Schroder Numbers to Higher Dimensions Publication date: Aug 23, 2004 Abstract: Let C(d,n) denote the set of d-dimensional lattice paths using the steps X_1 := (1, 0, ..., 0), X_2 := (0, 1, ..., 0), ..., X_d := (0,0, ...,1), running from (0,0, ... ,0) to (n,n, ...,n), and lying in {(x_1,x_2, ..., x_d) : 0 <= x_1 <= x_2 <= ... <= x_d }. On any path P:=p_1p_2 ... p_{dn} in C(d,n), define the statistics asc(P) := |{i : p_ip_{i+1} = X_jX_l, jl }|. Define the generalized Narayana number N(d,n,k) to count the paths in C(d,n) with asc(P)=k. We consider the derivation of a formula for N(d,n,k), implicit in MacMahon's work. We examine other statistics for N(d,n,k) and show that the statistics asc and des-d+1 are equidistributed. We use Wegschaider's algorithm, extending Sister Celine's (Wilf-Zeilberger) method to multiple summation, to obtain recurrences for N(3,n,k). We introduce the generalized large Schroder numbers (2^{d-1}sum_k N(d,n,k)2^k)_{n>=1} to count constrained paths using step sets which include diagonal steps. ============================== N13. S. Ole Warnaar: On the q-Analogue of the Sum of Cubes Publication date: Aug 23, 2004 Abstract: A simple q-analogue of the sum of cubes is given. This answers a question posed in this journal by Garrett and Hummel. _______________________________________________ Journal home page: www.combinatorics.org List management: http://cs.anu.edu.au/mailman/listinfo/ejc-list