Báo cáo toán học: "The weighted hook length formula III: Shifted tableaux" docx

... (2) Interestingly, the shifted hook length formula was discovered before the non- shifted one [Thr52]. Shortly after the fa mous G r eene-Nijenhuis-Wilf probabilistic proof of the ordinary hook length for ... 7, the hook length formula gives f 322 = 7! 5 · 4 · 1 · 3 · 2 · 2 · 1 = 21. 1 2 3 4 5 6 7 Figure 1: Young diagram [λ], λ = 66532, hook H 23 with hook length h 2...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 10:20

... Jensen [Jen71] produced a specific rectilinear drawing of K n for each n, which availed itself of a formula, denoted j(n), for the exact number of edge cross- ings. In particular, the electronic journal

Ngày tải lên: 07/08/2014, 06:22

... certain graph products, arXiv:math.CO/0410030, 2004. [7] A. Vuong and I. Wyckoff, Conditions for weighted cover pebbling of graphs, arXiv:math.CO/0410410, 2004. [8] N. Watson and C. Yerger, Cover ... all pebbles are on one single node. For two nodes v and u,thedistance d(v, u) from v to u is the length of the minimal path from v to u. (For a directed graph, d(v, u) = d(u, v) in general.)...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:20

... (λ)≤d (f λ ) 2 s λ (1 d ) χ λ (σ), where χ λ is the irreducible character of S n labelled by λ. The following integration formula was proved in [1]. Theorem 2. Let i, j, i  , j  : [n] → [d] be any functions. Then  U(d) u i(1)j(1) . ... most k rows whose terms count certain standard and semistandard Young tableaux. We combine our formula with a variant of the Colour-Flavour Transformat...

Ngày tải lên: 07/08/2014, 15:22

... On the other hand, the length distribution W (q)=  w∈W q l(w) does make sense in [[q]], and is known to be a computable rational function in q (see equation (6)). The formula for W (t, q) (equation ... indeterminate t s . One can also refine this computation to incorporate other statistics than the length function l(w), as long as the statistic n(w)inquestionisadditive under every parab...

Ngày tải lên: 07/08/2014, 06:20

... s λ [s µ ] at Hook Shapes If s λ [s µ ]=  ν a ν s ν , define s λ [s µ ]| hooks =  ν ahook a ν s ν . Then we have the following theorem. Theorem 3.1 1. s λ [s µ ]| hooks =0unless both λ and µ are hooks. 2. ... work we obtain explicit formulas when ν =(1 a ,b)(ahookshape),ν =(1 a ,b,c) (a hook plus a row), or ν =(1 a , 2 b ,c) (a hook plus a column). For example, the well-known formula...

Ngày tải lên: 07/08/2014, 08:20

... box in the diagram of λ, then the (i, j) -hook is the set of boxes in λ {(i, j  ):j   j}∪{(i  ,j):i   i}, We call the (i, i) -hook the i th principal hook. the electronic journal of combinatorics ... of the second principal hook with s +1, s +2, , t and fill the row with t +1,t +2, , x. Continuing in this way we form the hook tableau. Example 2.1. On the left is the hook table...

Ngày tải lên: 07/08/2014, 08:22