Báo cáo toán học: "A cluster expansion formula (An case" pdf

... any seed Σ in a Ptolemy cluster algebra, we present a formula for the expansion of an arbitrary cluster variable in terms of the cluster variables of the seed Σ. Our formula is given in a combinatorial way, ... our cluster expansion formula was also known to Carroll and Price [CP] and to Fomin and Zelevinsky [FZ3]. The author thanks Hugh Thomas for interesting discussions on...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 06/08/2014, 05:20

Ngày tải lên: 05/08/2014, 15:20

... establish the following formula |V | +  q∈V [d(q) − 2]l(v, q)=1 for any v ∈ V . Consequently, this enables us to evaluate the average distance of some particular trees. 2. The Formula Theorem 2.1. ... G.  3. The Average Distance The previous formula may be used to find the average distance in some special trees. Let us start by some preliminary results. A Formula About Tree 347 Step...

Ngày tải lên: 06/08/2014, 05:20

... A Plethysm Formula for p µ (x) ◦ h λ (x) William F. Doran IV Department of Mathematics California Institute ... 91125 doran@cco.caltech.edu Submitted: September 10, 1996; Accepted: May 2, 1997 Abstract This paper gives a new formula for the plethysm of power-sum symmetric functions and complete symmet- ric functions. The ... ω maj µ t (T ) is a root of unity which de- pends on µ, t, and T...

Ngày tải lên: 07/08/2014, 06:20

... H. Bass, E. H. Connell, and D. Wright, The Jacobian conjecture: Reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. (N.S.) 7 (1982) 287–330. [2] E. A. Bender and L. ... Univ. Press, 1998. [4] I. M. Gessel, A combinatorial proof of the multivariate Lagrange inversion formula, J. Combin. Theory Ser. A 45 (1987) 178–195. [5] I. P. Goulden and D. M. Kulkarni, Multiv...

Ngày tải lên: 07/08/2014, 06:22

... to ⇐ ,too. the electronic journal of combinatorics 9 (2002), #R18 9 A ‘nice’ bijection for a content formula for skew semistandard Young tableaux Martin Rubey Institut f¨ur Mathematik Universit¨at ... be found at http://www-math.mit.edu/~rstan/ec. Stanley took it from [1], Theorem 3.1, where the formula is stated incorrectly, too. the electronic journal of combinatorics 9 (2002), #R18 1...

Ngày tải lên: 07/08/2014, 06:23

... equality (6) follows.  the electronic journal of combinatorics 10(2003),#R9 6 A p, q-analogue of a Formula of Frobenius Karen S. Briggs Jeffrey B. Remmel Department of Mathematics University of California, ... 246-275) used rook configurations to give a combinatorial interpretation to the q-analogue of a formula of Frobenius relating the Stirling numbers of the second kind to the Eulerian...

Ngày tải lên: 07/08/2014, 07:21

... summa- tion formulas for sums of m-th power for m =1, 2, ,11. In particular, for 1 ≤ m ≤ 5 we recover the formulas (1.2)–(1.6) of Warnaar and Schlosser. For m =6, 7, ,11 we obtain the following formulas ... summation formulas of (1.1) for m ≤ 11. Section 5 contains some further extensions of these sum- mation formulas. 2 Some Preliminary Lemmas The following is our first step towards our summa...

Ngày tải lên: 07/08/2014, 08:22

... first formula. For the second formula, we note that L =1− K −1 , and a formula for the coefficients of K −1 follows from (8.4) and (5.10). Applying Lemma 2.5 to Theorem 8.3 gives hook length formulas ... P n (a, b, c). Moreover, each type of forest or tree has a hook length formula analogous to Postnikov’s. (Some of these hook length formulas have been found earlier by Du and Liu [5].) A...

Ngày tải lên: 07/08/2014, 08:22