Báo cáo toán học: " Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted" pptx

... 1995 Bijective proofs of the hook formulas for the number of ordinary standard Young tableaux and for the number of shifted standard Young tableaux are given. They are formulated in a uniform ... provide a bijective proof of the hook formula for the number of shifted standard Young tableaux (and its q-analogue; see the Theorem in...

Ngày tải lên: 07/08/2014, 06:20

... the modified involution φ is an involution on the set of improper forests of colored binary trees, which reverses the parity of the color numbers of the forests. Hence the right side summand of ... trees and the set of colored 5-ary trees. The generalization of the parity reversing involution and the bijection to forests of colored binary trees and for...

Ngày tải lên: 07/08/2014, 15:22

... where i is the number of the IMF; j is the number of the iteration and g is the number of pyramid layer. In the first itera- tion, h (1,1) (p g ,q g )istheoriginalreducedimageX(p g ,q g ). The reduced ... μ M ] 2 . (12) where C is the coefficient of correlation, F(i, j)andM (i, j)arethegrayvalueofthefusedandMSimages, respectively. μ F is the mean of fused i...

Ngày tải lên: 20/06/2014, 20:20

... Exposition of identities and proofs The origin of this paper was the attempt to give a bijective proof of the following identity for Schur functions, which arose in work of Kirillov [10]: Theorem ... notation as Theorem 2 in [15], together with another elegant proof. Moreover, the bijective method yields a proof of the second author’s theorem [11, Theorem 3.2]: S...

Ngày tải lên: 07/08/2014, 06:22

... departments for the extensive use of their computers and especially the group of Prof. Wachsmuth at the Technische Fakult¨at in Bielefeld for the opportunity to run a lot of jobs on their machines. ... algorithm The central tool for the computation of the remaining 261071 Ramsey numbers r(K 3 ,H) for connected graphs H of order 9 and the further Ramsey nu...

Ngày tải lên: 07/08/2014, 06:22

... theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the ... q 2 ) n = ∞  n=0 D(n)q n . the electronic journal of combinatorics 18 (2011), #P60 16 As in the proof of the previous theorem, we do this for the second identity...

Ngày tải lên: 08/08/2014, 14:22

... 0, and then h  (t) ≤ 0, so f (t) is concave on (0, 1). NEW PROOFS OF SCHUR-CONCAVITY FOR A CLASS OF SYMMETRIC FUNCTIONS HUAN-NAN SHI ∗ , JIAN ZHANG AND CHUN GU DEPARTMENT OF ELECTRONIC INFORMATION,TEACHER’S ... = 1, . . . , n, (4) and established the following results by using Theorem A. NEW PROOFS OF SCHUR-CONCAVITY FOR A CLASS OF SYMMETRIC FUNCTIONS 7 [2] Wang, B...

Ngày tải lên: 20/06/2014, 21:20

... K)=−w(G  ,K  ). In the second case the entries in the i-th column (i, j, i, 1) satisfy the inequalities i +1≤ j ≤ n,whilethej-th column (on the right of the i-th column) is of the form (a j ,b j ,j,0). Then ... Let (k,l)beanother link of G such that k ∈ K.Thenk<iby definition of i. On the other hand, l = j.Ifl = i,then(k, l)remainsalinkofG  .Ifl = i,then (b k ,k...

Ngày tải lên: 07/08/2014, 06:20

... one of the two other cases. The successor of the end of e 0 in M is the same as in M  since the start and the end of e 0 are adjacent. Therefore ψ(M) is obtained from ψ(M  ) by exchanging the ... by cutting e 1 , A 1 being the one which contains the start of e 1 and A 2 its end. The end of e 0 is the last leaf of A 1 before e 1 . Therefore when e 1 is...

Ngày tải lên: 07/08/2014, 06:20

... at the position of the letters b and b in w. More precisely, we read the word w and while making the tour of T according to the letters a, a, we insert heads for the letters b and tails for the ... the same as the number of u (resp. v) in S, - the number of inactive leaves lying between the i th and i + 1 th active leaves in B is the size of...

Ngày tải lên: 07/08/2014, 15:22