Báo cáo toán học: "An elementary proof of the hook formula" ppt

... (5) The proof of (3) is completely combinatorial, the proof of (4) uses nothing more than the fundamental theorem of algebra, and the proof of (5) is a simple geometric argument. Proof of (3). The ... hooks in the diagram of λ. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing mor...

Ngày tải lên: 07/08/2014, 15:23

... A proof of the Kahn-Lov´asz theorem The entropy proof of the Kahn-Lov´asz theorem is complicated by the fact that there can be edges of the graph (and a fixed matching) amongst the neighbors of ...  E is independent of the event {x  V y}. Proof. For any permutation of the edges of m, there is a permutation of V (G) inducing it. Therefore, the uniformity...

Ngày tải lên: 08/08/2014, 12:23

Ngày tải lên: 05/08/2014, 09:46

... ···(x−n+1). Then we have the following reciprocity theorem. Theorem. For any board B ⊂ [d] × [d], R(B; x)=(−1) d R(B; − x − 1). The existing proofs derive this as a corollary of other reciprocity theorems, ... subset of [d] × [d](where[d]isdefinedtobe{1, 2, ,d})andtherook numbers r B k of a board are the number of subsets of B of size k such that no two elements have the sa...

Ngày tải lên: 07/08/2014, 06:20

... extension of the Littlewood-Richardson rule [Z]. Taking the specialization λ = , we obtain the decomposition of s µ/ν into Schur functions; it is simpler than the traditional formulation of the Littlewood-Richardson rule ... b i free k + 1’s in row i of T , then there should be b i free k’s and a i free k + 1’s in row i of σ k (T ). In the following, T ≥j denotes the s...

Ngày tải lên: 07/08/2014, 06:23

... number of boxes in the first row is equal to the size of the first part, the number of boxes in the second row is equal to the size of the second part, etc. For example, the Ferrers diagram for the ... that the set S consists of pairs of partitions with no primed parts. In the definition of φ −1 when there is a primed integer in the image, we consider only...

Ngày tải lên: 07/08/2014, 08:20

... of the hive give λ • the differences on the Northeast side of the hive give µ • the differences on the South side of the hive give ν where all differences are computed left-to-right throughout the ... vertex. The constant coordinate assigned is then the label on ∆ counterclockwise of the extra vertex, minus the label on ∆ clockwise of the extra vertex. The v...

Ngày tải lên: 07/08/2014, 08:20

... me to the area of log-concave sequences. Abstract We provide a combinatorial proof for the fact that for any fixed n, the sequence {i(n, k )} 0≤k ≤ ( n 2 ) of the numbers of permutations of length ... i(p) of inversions, and the study of numbers i(n, k)ofn-permutations having k inversions, is a classic area of combinatorics. The best-known result is the following...

Ngày tải lên: 07/08/2014, 08:22

... 1986. the electronic journal of combinatorics 12 (2005), #R18 8 Theorem 2.3 (Aztec diamond theorem) The number of domino tilings of the Aztec diamond of order n is 2 n(n+1)/2 . Remark: The proof of ... Kirkland [2] give a proof by considering a matrix of order n(n +1) the determinant of which gives a n . Their proof is reduced to the computation of the dete...

Ngày tải lên: 07/08/2014, 08:22

... depends on the ratio of interelement spacing of the array to the wavelength. In the case that the angle ambiguity occurs, we refer to [14-16] for resolving the ambiguity. The remainder of this article ... it is believable that the number of the selected principle components i n step (b) of Table 2 is equal to the num- ber of the actual sources ; for lower SNR...

Ngày tải lên: 20/06/2014, 20:20