Báo cáo toán học: "Combinatorial statistics on type-B analogues of noncrossing partitions and restricted permutations" ppt

... 10 2 Statistics on type-B noncrossing partitions We begin by defining B -analogues of the set partition statistics described in section 1.1, valid for noncrossing partitions of type B. 2.1 The statistics ... signed permutations, is of special interest here and is further considered in Section 4. 4 Relations between statistics on type-B noncross- ing partitions...

Ngày tải lên: 07/08/2014, 06:20

... for l ∈ U and β m (1) = n for m ∈ V . Then, the map f (r) × g (s) consisting of r copies of the component bijection f and s copies of the component bijection g along with judicious use of the analysis ... distributions of (iddes; des,comaj, des, comaj) and (iddes; ris, corin, ris, corin) for unrestricted and restricted pairs in S 2 n .The corresponding refined bibasic Besse...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 05/08/2014, 15:21

... interesting classification of weak amenability of Beurling algebras in term of functions defined on G. Theorem 1.1. [2, Theorem 2.23] Let  1 (G, ω) be a weighted non-ab elian group algebra and let {C i } i∈I be ... and let {C i } i∈I be the partition of G into conjugacy classes. For each i ∈ I,letF i denote the set of nonzero functions ψ : G → C which are supported on C i an...

Ngày tải lên: 06/08/2014, 05:20

... representation by sumsets and subset sums, J. Num- ber Theory 62 (1997), 127–143. the electronic journal of combinatorics 7 (2000), #R30 6 Observe that H is increasing on (1, 2] and decreasing on [2, ... k>,ifthere are no solutions to the equation x 1 + ···+ x k = y 1 + ···+ y  in A. Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the...

Ngày tải lên: 07/08/2014, 06:20

... A note on the ranks of set-inclusion matrices D. de Caen Department of Mathematics and Statistics Queen’s University Kingston, Ontario, Canada K7L 3N6 decaen@mast.queensu.ca Submitted: ... relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1)-matrix of incl...

Ngày tải lên: 07/08/2014, 06:22

... Academic Press, London, 1978. [2] R.A. Brualdi, Matrices of zeros and ones with fixed row and column sum vectors, Linear Algebra Appl. 33 (1980), 159-231. the electronic journal of combinatorics ... and j = ρn +1, ,2ρn.Denotethisblock M 2 .DenotebyM 3 the block consisting of the rows i = |A + |+1, ,m and the columns j =1, ,ρn.DenotebyM 4 the block consisting of the rows i = |A...

Ngày tải lên: 07/08/2014, 06:23

... ˜w 4 ˜w 5 ˜w 6 ˜w 7 ,itmustbe that m = 3 and the subword to the left of the leftmost 6 in w contains two 0’s, two 1’s, and two 2’s. However, w 1 must consist of 0 and 1 in some order, and w 2 of 1 and 2, so the two ... of (k − 1)’s in w m , one must be on the left half of s m and hence before the m in h m+1 ,and the other must be on the right half of s k−1 and...

Ngày tải lên: 07/08/2014, 08:20

... 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. In [2] Chen and Liu construct ... 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;...

Ngày tải lên: 07/08/2014, 08:22

... Bergeron and C. Hohlweg, Coloured peak algebras and hopf algebras, arXiv: math.AC/0505612. [3] C. Bonnaf´e and C. Hohlweg, Generalized descent algebra and construction of irre- ducible characters of ... Classifications: 05E99, 16S34 Abstract In the context of generating functions for P -partitions, we revisit three flavors of quasisymmetric functions: Gessel’s quasisymmetric fun...

Ngày tải lên: 07/08/2014, 13:21