Báo cáo toán học: "A Combinatorial Proof of the Log-concavity of a famous sequence counting permutations" potx

... comments and suggestions which have led to a substantially improved paper. An Asymptotic Expansion for the Number of Permutations with a Certain Number of Inversions Lane Clark Department of Mathematics Southern ... =3)and(6;m =1) the electronic journal of combinatorics 7 (2000), #R50 11 References [1] M. Abramowitz and I .A. Stegun, Eds., Handbook of Mathematical Functions...

Ngày tải lên: 07/08/2014, 06:20

... result and the one just quoted, one obtains bijections that map any pair of statistics (area, dinv), (dmaj, area  ), (pmaj, area) to any other. As a corollary, we obtain bijective proofs that all ... pairs of statistics (area, h)and(pmaj, area)havethe same bivariate distribution on labelled paths. Therefore, all three statistics have the same univariate distribution. Unfortunately,...

Ngày tải lên: 07/08/2014, 08:20

... we obtain the order of H as appears in (4). Remark. It is easy to see that the diameter of a k-regular graph of order v is at least log k−1 v and that the random k-regular graph has diameter ... USTIMENKO Department of Mathematics and Mechanics University of Kiev, Kiev 252127, Ukraine; vau@trion.kiev.ua A. J. WOLDAR Department of Mathematical Sciences Villanova University...

Ngày tải lên: 07/08/2014, 06:22

... the later terms are quite complicated. In the final section of our paper, we present a generalization of the first equality in Theorem 1. 2 Discussion of Theorem 2 We shall not give a proof of this ... which agrees with the right side. More generally, we may replace the graph K n on the left with an arbitrary graph G,and then on the right we replace the displayed p...

Ngày tải lên: 07/08/2014, 06:22

... if 8a( a −1) is a square, then so is a( a −1)/2isasquareaswell,buta (a −1)/2 is a triangular number. In other words, 8a( a −1) is a square if and only if the triangular number a( a − 1)/2 is a square. ... a 2 − 2a is a triangular number. In other words, 8a 2 − 1 6a + 1 is a square if and only if a 2 − 2a is triangular. If we set a = a − 1, then a 2 − 1 =a 2 − 2a,...

Ngày tải lên: 07/08/2014, 08:20

... methods in the Theory of m-Quasi-Invariants J. Bell, A. M. Garsia and N. Wallach Department of Mathematics University of California, San Diego, USA agarsia@math.ucsd.edu Submitted: Jan 29, 2005; Accepted: ... action of s 12 and s 23 . However, since all of them are images of δ 12 there are automatically s 12 - invariant. Thus we only need to assure that they are also s 23 -inva...

Ngày tải lên: 07/08/2014, 08:22

... Mathematics 54187 Sakarya/ TURKEY rkeskin@sakarya.edu.tr Bahar Demirt¨urk Sakarya Univers ity Faculty of Science and Arts Department of Mathematics 54187 Sakarya/ TURKEY demirturk@sakarya.edu.tr Submitted: ... that A −1 T A and B −1 SB have the same order and therefore T and S have the same order. That is, the two circuits have the same length. A circuit o f length 3, 4, and...

Ngày tải lên: 08/08/2014, 01:20

... k n (σ)  . ∗ The final version of this paper was written during the author’s stay at Institute o f Statistical Science of Academia Sinica , Taipei. We gratefully acknowledge the support and thank Professors ... permutations, Ann. Probab., 1992, 20, 3, 1567–1591. [2] R. Arratia, A. D . Barbour and S. Tavar´e, Logarithmic Combinatorial Structures: a Probabilistic Approach, EMS Mo...

Ngày tải lên: 08/08/2014, 12:22

... M. Deza and P. Frankl. On the maximum number of permutations with given max- imal or minimal distance. Journal of Combinatorial Theory (A) , 22:352–360, 1977. [11] Michael Deza and Tayuan Huang. ... characters of S n are available on programs as Magma [5] or GAP [13]. Using the “linprog” ro utine of Matlab [14], we obtain the bounds in Table 1. Note that the linear programmi...

Ngày tải lên: 08/08/2014, 12:22

... Special Administrative Region of the People’s Republic of China. References [1] M. Abramowitz and I .A. Stegun. Handbook of mathematical functions with formulas, graphs, and mathematical tables, ... 2 Generalized Bell polynomials and the combinatorics of Poisson central moments Nicola s Privault Division of Mathematical Sciences School of Physical and Mathematical Sciences Nan...

Ngày tải lên: 08/08/2014, 14:22