Báo cáo toán hoc:" Permutation Statistics and q-Fibonacci Numbers " doc

... counted by the Fibonacci numbers. These distribu- tions will give us q-Fibonacci numbers which are related to the q-Fibonacci numbers of Carlitz [2], Cigler [3, 4], and Goyt and Sagan [6]. Let the ... produced a class of q-Fibonacci numbers , which they related to q-Fibonacci numbers studied by Carlitz and Cigler. In this paper we will study the d istributions of some M...

Ngày tải lên: 08/08/2014, 01:20

... π 1 is a permutation of the set {n − k +1, ,n−1} ,and 2 is a permutation of the set {1, ,n−k}. Furthermore, π 1 and π 2 are each (132)-avoiding. Conversely, if π 1 and π 2 are (132)-avoiding permutations ... B´ona, Permutations with one or two 132-subsequences. Discrete Math. 181 (1998), no. 1-3, 267–274. [2] Aaron Robertson, Permutations containing and avoiding 123 and 132 patte...

Ngày tải lên: 07/08/2014, 06:20

... k.Ifn 3 =2andt k =5,thenwe are covered by Sublemma 4.3. If n 3 =1,n 2 ≥ 2andt k ≥ 6letu = 6and = (0 2)(1 4)(3 5) and apply Sublemma 4.1. If n 3 =1,n 2 = 1 or 2, and t k =5,letσ k = (0 3)(2 4)(1) and ... gives one permutation with separations u u 0 1 . As v ≥ 3, u ≥ 7andsou +4≤ 2(u − 1) and v +1<u− 2. Then Lemma 5 gives two permutations with separations (u − 1) u+4 and three gap...

Ngày tải lên: 07/08/2014, 08:20

... Babson and E. Steingr´ımsson, Generalized permutation patterns and a classifica- tion of the Mahonian statistics, S´em. Lothar. Combin. 44 (2000), B44b. [2] A. Burstein, On some properties of permutation ... #R108. [6] S. Corteel and J. S. Kim, Combinatorics on permutation tableaux of type A and type B, European J. Combin. 32 (2011), 563-579. [7] S. Corteel and P. Nadea u, Bij...

Ngày tải lên: 08/08/2014, 14:23

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Ngày tải lên: 05/08/2014, 15:20

... integers, on the one hand, and Wythoff’s Game [9, 39, 11, 1, 8] on the other. Wythoff’s Game is played with two heaps from which players alternately take any number from one heap or equal numbers from each; ... [37], Multivision [26], partizan octal and subtraction games [38] and extensions of Conway’s ‘short games’ [52]. He has been especially interested in annihilation games [10, 53,...

Ngày tải lên: 07/08/2014, 06:23

... cases are similar, and R g,h satisfies conditions 1 and 2. The conditions 1, 2, and 3 recursively define R g,h , which proves the uniqueness of the function R g,h . Suppose that g(x)andh(x) are functions ... that g(x),h(x) =0,andthat f(M,x,y,{z e  } E ) is a function which satisfies conditions 2 and 3 for all M∈A.LetF 0 and F 1 denote the terms f(U 0,1 ,x,y,z e ) − h(z e ) g(z e ) a...

Ngày tải lên: 07/08/2014, 06:23

... n.LetI B and I S be subsets of [k] and let B = {C i : i ∈ I B } and S = {C i : i ∈ I S }. We refer to the sets B and S as the bases and summits of G respectively. A set C i ∈BiscalledabaseofG and ... line, and then we connect n to the lefthand endpoint of the first cycle, the righthand endpoint of each cycle to the lefthand endpoint of the cycle following it, and we connect the...

Ngày tải lên: 07/08/2014, 06:23

... follows from Theorem 2 and item 4 above. ✷ Corollary 1 There exists a partition of n with BG-rank = j if and only if j + n is even and j(2j − 1) ≤ n. 4 Congruences Berkovich and Garvan’s motivation ... combinatorics 13 (2006), #N18 2 References [1] Alexander Berkovich and Frank Garvan, On the Andrews-Stanley refinement of Ra- manujan’s partition congruence modulo 5 and generalizati...

Ngày tải lên: 07/08/2014, 13:21

... Factors and Factorization. 403–430. Handbook of Graph Theory ed. J. L. Gross and J. Yellen. CRC Press, 2003, ISBN: 1-58488-092-2. [11] W. R. Pulleyblank, Matchings and Extension. 179–232. Handbook ... journal of combinatorics 13 (2006), #R59 9 Total domination and matching numbers in claw-free graphs 1 Michael A. Henning ∗ and 2 Anders Yeo 1 School of Mathematical Sciences Univers...

Ngày tải lên: 07/08/2014, 13:21