Báo cáo toán học: " A NEW CONSTRUCTION FOR CANCELLATIVE FAMILIES OF SETS" doc

... the union of any element of F 1 with any element of F 2 . It is easy to see that the product of two cancellative families is also a cancellative family ( (A 1 ,A 2 ) ∪(B 1 ,B 2 )= (A 1 ,A 2 ) ∪(C 1 ,C 2 ) ... ask how large cancellative families can be. We define f(n) to be the size of the largest possible cancellative family of subsets of a n-set and f(k,n)...

Ngày tải lên: 07/08/2014, 06:20

... National University Daegu 702-701, South Korea Full list of author information is available at the end of the article Abstract This paper performs a further investigation on the q-Bernoulli polynomials and numbers ... polynomials and show some properties. That is, A ikgöz et al. introduced a new generating function related the q-Bernoulli polyno- mials and gave a new construct...

Ngày tải lên: 21/06/2014, 00:20

... Acknowledgment The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The author also thanks Prof. Cheng Zhao for his advice. References [1] J .A. Bondy and U.S.R. ... Chunhui Lai, On the size of graphs with all cycle having distinct length, Discrete Math. 122(1993) 363-364. [6] Chunhui Lai, The edges in a graph in which no two cycles have the same length, J....

Ngày tải lên: 07/08/2014, 06:22

... The Netherlands 2003. [9] Suparta, I N. and A. J. van Zanten, A note on balanced Gray codes”, submitted for publication. [10] A. J. van Zanten and I N. Suparta, “Totally balanced and exponentially balanced Gray ... A simple proof for the existence of exponentially balanced Gray codes I Nengah Suparta ∗ Department of Applied Mathematics Faculty of Electrical Engineering, Mathema...

Ngày tải lên: 07/08/2014, 08:22

... then because λ and µ agree to the left of column c, λ/µ cannot contain any cells in or below row r, and we already have that λ and µ agree above row r, so we are left with the conclusion that λ ... Ferrers diagram of λ, which we often identify with λ, consists of  left-justified rows where row i contains λ i cells. An inner corner in this diagram is a cell whose removal leaves the dia...

Ngày tải lên: 07/08/2014, 15:22

... Operation (β) adds a new row above the row containing d i (of the same length), and a new column on the right of c n , made of i cells, as illustrated in Figure 8. Observe that, since the new added ... semi-perimeter. A simple algebraic computation leads then to the determination of generating functions for the two classes. In [1] it is also shown that an ECO constructi...

Ngày tải lên: 07/08/2014, 15:22

... a 1 ) − n  j=3  a 1 a j (1 + a − a 1 )(1 + a − a 1 − a j ) + a 1 a j a( a − a 1 )   C n (a) =  a 1 1 + a − a 1 − a 1 a 2 a( a − a 1 ) − a 1 (a − a 1 − a 2 ) a( a − a 1 ) − n  j=3 a 1 a j (1 + a − a 1 )(1 ... ., a j−1 , a j − 1, a j+1 , . . . , a n )  − CT x x 2 2 x 1 x j D n (x, a) =  a 1 + a j − 1 1 + a − a 1...

Ngày tải lên: 08/08/2014, 11:20

... A short proof for the number of permutations containing pattern 321 exactly once Alexander Burstein Department of Mathematics Howard University Washington, DC 20059 USA aburstein@howard.edu Submitted: ... USA aburstein@howard.edu Submitted: May 30, 2011; Accepted: Aug 23, 2011; Published: Sep 2, 2011 Mathematics Subject Classification: 0 5A0 5, 0 5A1 5 Abstract We give a short proof...

Ngày tải lên: 08/08/2014, 14:23

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Ngày tải lên: 05/08/2014, 09:46

... electronic journal of combinatorics 14 (2007), #R6 17 4.1 Satisfiability solving The construction of a Van der Waerden certificate can easily be formulated as a satis- fiability (Sat) problem. As mentioned ... n} of the partition. The transformation involved is called a circular translation. Cyclic certificates have the favorable property that they can be repeatedly appended to crea...

Ngày tải lên: 07/08/2014, 15:22