Báo cáo toán học: "Coding parking functions by pairs of permutations" docx

... new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length n and the set of parking functions of length ... Coding parking functions by pairs of permutations Yurii Burman Independent University of Moscow, 121002, 11, B.Vlassievsky per., Moscow, Russia burman@mccme.ru Michae...

Ngày tải lên: 07/08/2014, 07:21

... number of parking functions of length n is (n + 1) n−1 and the number of primitive parking functions of length n is the Catalan number 1 n+1  2n n  , see [10]. A primitive parking function of length ... and a parking function is a permutation of a primitive one. The (n n ) -parking functions are called “type B parking functions in [4]. The enumeration of µ/ν...

Ngày tải lên: 07/08/2014, 21:21

... hyperoctahedral group B n by Adin, Brenti and Roichman, and for the group of even-signed permutations D n by Biagioli. We prove analogues of MacMahon’s equidistribution theorem for the group of signed even ... journal of combinatorics 11 (2004), #R83 8 Definition 3.17. 1. The S-descent set of σ ∈ B n is defined by Des S (σ):={ 1 ≤ i ≤ n − 1 | σ(i) >σ(i +1)}. 2. Define the majo...

Ngày tải lên: 07/08/2014, 08:22

... 2 The proof of the Theorem The q-difference operator and the q-shift operator η are defined by D q {f(a)} = 1 a (f(a) − f(aq)) and η{f (a)} = f (aq), respectively. ... q) ∞ · E(eθ) {(abcd, bcdf; q) ∞ } . (7) the electronic journal of combinatorics 12 (2005), #N3 2 Again, applying the results (3) and (4) of Chen and Liu, we have E(eθ)  (q −n bc, bd; q) ∞  = (q −n bc, ... q) ∞ (ac,ad,cf...

Ngày tải lên: 07/08/2014, 08:22

... conditions of Proposition 7.5, and hence 423516 ∈ SS 6 . Next, we consider the sum of coefficients of ˆ Φ n (c, −d). Theorem 7.6. The sum of coefficients of ˆ Φ n (c, −d) is |R n |. Proof. The sum of coefficients ... also think of a loose edge directed to the right coming out of the rightmost vertex of every tree T i (σ) including T n (σ) = T (σ) — this way the number of edges c...

Ngày tải lên: 07/08/2014, 21:20

... well [31]. The XPS data of Zn2p and Mn2p further provide evidences for the incorporation of Mn 2+ ions into ZnO. To obtain a better understanding of the formation of Mn-doped ZnO HMSs, a ... depicts the formation process of Mn-doped ZnO nanoparticles due to the reducing capacity of EG. According to the report, acetaldehyde (CH 3 CHO) is produced by dehydration of EG at...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... for all x ∈ D. (18) Proof. Since the only difference between the assumptions of Proposition 8 and of Proposition 9 is the substitution of (13) by (18), almost all the proof of Proposition 8 can ... γ-convexity of some classes of disturbed functions. As consequence, these disturbed functions inherit the mentioned optimization properties of roughly convex functions. Such a r...

Ngày tải lên: 06/08/2014, 05:20