Báo cáo toán học: "A Combinatorial Formula for Orthogonal Idempotents in the 0-Hecke Algebra of the Symmetric Group" potx

... if i = N, π i if i = N. the electronic journal of combinatorics 18 (2011), #P28 15 A Combinatorial Formula for Orthogonal Idempotents in the 0-Hecke Algebra of the Symmetric Group Tom Denton Submitted: ... automorphism of the un- derlying graph of a Dynkin diagram induces an auto morphism of the Hecke algebra. For the Dynkin diagram of S N , there...

Ngày tải lên: 08/08/2014, 12:23

... to the product of the weights of each of its entries, here the weight of entry s in T is taken to be the weight of the corner square containing s in the pa rt itio n obtained from the shape of ... is the the number of columns of height equal to the height of the column of i in the tableau obtained by removing all the entries j > i from T ,...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:20

... well-defined. The choices for the initial position of F in each iteration might effect the outcome of the algorithm. But, it has been shown (see Section 3.9 of [S] for a proof) that for all choices of the F’s, ... choices of the F’s, the resulting J(T ) is the same. The next result gives an important property of the Jeu de Taquin operation. A proof is giv...

Ngày tải lên: 07/08/2014, 06:20

... the cells of the polyomino; U2 : the lowest cell of the rightmost column of the polyomino has the minimal ordinate among all the cells of the polyomino. We say that a convex permutomino P belongs ... a combinatorial interpretation of the closed formula (10) for the number of con- vex permutominoes. We remark that the expression of f n resembles the...

Ngày tải lên: 07/08/2014, 15:22

... be the number of cells (including the possible circle at the end of the row) to the right of s. Let a lso ℓ Λ (s) be the number of cells (not including the possible circle at the bottom of the ... ecture of [3] giving a closed form f ormula for the norm of the Jack polynomials in superspace with respect to a certain scalar product. The proof is mainly...

Ngày tải lên: 07/08/2014, 21:21

... from Eq. (4) in [22]. 2 In the derivation, the value of k appears in relation to the geometry of FPLs, and the exact range of k for which the formula is pr oved is not made clear. In the present ... containing solely nonpositive powers of the u i since otherwise they do not con- tribute to the contour integral. Now expanding the product in brackets we n...

Ngày tải lên: 08/08/2014, 12:22

... defined to be the smallest integer t , such that in any k-coloring of the edges of K t , there is a complete subgraph K n all of whose edges have the same color. A sum-free partition of [1 ,s ] ... is the more important term in the func- tion. For the case n = 160 and k = 5 we obtained best results when c 1 /c 2 was allowed to randomly vary in the range 2 12 to 2...

Ngày tải lên: 07/08/2014, 06:20

... Whitehead (Theorem 2.1 in [9]) gave a close, though intricate, formula for k(λ, µ , ν) valid for any λ of length at most 4; M. Ro sas (Theorem 1 in [10]) gave a formula of combinatorial nature for k(λ, ... result with this simple formula we obtain a new one. For completeness we record here the Remmel-Whitehead formula in the equivalent version of Rosas. In...

Ngày tải lên: 07/08/2014, 21:21

... [4] gave another proof of (3). The main purpose of this paper is to prove (3) combinatorially. In the meanwhile, we get as corollaries the results of Bruns and Hibi [2] : a formula of b k (∆) ... nontrivia l property of trees which was observed by Bruns and Hibi [2]. the electronic journal of combinatorics 17 (2010), #R9 6 A combinatorial proof of a formula for...

Ngày tải lên: 08/08/2014, 11:20