Báo cáo toán học: " A Two Parameter Chromatic Symmetric Function" potx

... Generalization of the Chromatic Polynomial of a Graph. Adv. Math. 111. 1995. 166-194. [7] R. Stanley. Graph Colorings and Related Symmetric Functions: Ideas and Applica- tions. Discrete Math. ... 2004; Accepted: Jan 29, 2007; Published: Feb 12, 2007 Mathematics Subject Classification: 05C88 Abstract We introduce and develop a two- parameter chromatic symmetric function for a s...

Ngày tải lên: 07/08/2014, 15:22

... if they are equal) into the hole h and make the vacated square the new hole. T  is again a semistandard punctured tableau. Given a semistandard punctured tableau (T,h), one can repeat slides ... following two statements: (a) ABCD can contain an × only if Λ (A) =Λ(B)=Λ(C). (b) If Λ (A) k ⊃ Λ(B)=Λ(C), then k>1. To see (a) , first recall that an × canappearonlyonceineachrowandeachcolu...

Ngày tải lên: 07/08/2014, 08:22

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:20

... {a, b} ∗ → {a, b} ∗ by h (a) =ab, h(b)=ba. Let l = aabaab. Thus l R = baabaa. We see that the prefixes of l which are suffixes of l R are exactly a, aa, aabaa. Lemma 2.6 Word l is avoided by h ω (a) . Proof: ... otherwise aaa appears in m j , a contradiction since m j is overlap-free. Since aab is a prefix of m i ,f(aab)=aaf(b)isaprefixofm j . However, another prefix of m j is aabaab. Thus on...

Ngày tải lên: 07/08/2014, 06:20

... A Note on the Symmetric Powers of the Standard Representation of S n David Savitt 1 Department of Mathematics, Harvard University Cambridge, MA 02138, USA dsavitt@math.harvard.edu Richard ... USA dsavitt@math.harvard.edu Richard P. Stanley 2 Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139, USA rstan@math.mit.edu Submitted: January 7, 2000; Accepted: Fe...

Ngày tải lên: 07/08/2014, 06:20

... symbols. A subset of this matrix can be used for systems that are smaller than 4 × 4. This matrix pattern can also be extended to accommodate systems with more antennas. P = ⎡ ⎢ ⎢ ⎣ a −aa a aa−aa aaa a −aaaa ⎤ ⎥ ⎥ ⎦ (16) In ... constant througho ut the duration of each trial. 3.1 Rayleigh flat fading channels Rayleigh flat fading channels are the easiest channels to compensate. They co...

Ngày tải lên: 20/06/2014, 21:20

... the tableau decreases by 1 when the labels are decreased. A tableau that has a label of 2 lying above the 1 can be transposed about the diagonal and this tableau is isomorphic to a tableau of ... is the tableau that is flipped about the diagonal. Each standard tableau has either the label of 2 lying to the immediate right of 1 or above it. A tableau that has a 2 that lies immediately...

Ngày tải lên: 07/08/2014, 06:22

... 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. Zhan...

Ngày tải lên: 07/08/2014, 06:22

... Molina Department of Mathematics and Computer Science Alma College 614 W. Superior St. Alma MI, 48801 molina@alma.edu Ken W. Smith Department of Mathematics Central Michigan University Mt. Pleasant, ... A Proof of the Two- path Conjecture Herbert Fleischner Institute of Discrete Mathematics Austrian Academy of Sciences Sonnenfelsgasse 19 A- 1010 Vienna Austria, EU herbert.fleischner@oeaw.a...

Ngày tải lên: 07/08/2014, 06:23