Báo cáo toán học: "Recognizing Cluster Algebras of Finite type" doc

... study positivity [1]. One of the most striking results in the theory of cluster algebras due to S. Fomin and A. Zelevinsky is the classification of cluster algebras of finite type, which turns ... The proof of Lemma 3.5 is more involved, therefore, for the convenience of the reader, here we discuss an outline of our proof in some detail. To prove this lemma we assume, with...

Ngày tải lên: 07/08/2014, 15:22

Ngày tải lên: 05/08/2014, 15:21

... W of indices write A W for the submatrix of A consisting of all rows and columns index with elements of W . It is easy to see by inspection that each of the blocks Adj(A) γ i (a) is of one of ... class of τ 0,γ is an orbit of g d/d  1 . Hence the equivalence classes of τ 0,γ are the orbits of g d/d  1 , and, therefore, they are orbits of g d/d  . Thus, each eq...

Ngày tải lên: 07/08/2014, 06:22

... define the union of these with any cluster to be an extended cluster. We define a cluster monomial to be a product of nonnegative powers of cluster variables, and integer powers of frozen variables, ... cluster algebra has a distinguished set of generators called cluster variables which are grouped into overlapping subsets called clusters. Those cluster algebras generat...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 09:46

... whose bias corresponds to the ratio of the cardinalities of two distributive lattices, namely, the lattice of order ideals of P containing x and the lattice of order ideals of P not containing x. This ... proof of a formula for the number of Young Tableaux of a given shape, Adv. in Math. 31 (1979), 104–109. [GNW2] C. Greene, A. Nijenhuis and H. Wilf, Another probabilistic me...

Ngày tải lên: 07/08/2014, 06:22

... as the product of all parts of all partitions of n. It also equals b n , which is defined as the product of all factorials of all multiplicities of parts in partitions of n. Proofs of this may be ... be the number of partitions of n. The number p ∗ (n) of regular partitions of n equals the number of class regular partitions of n and then p  (n)=p(n) − p ∗ (n) is th...

Ngày tải lên: 07/08/2014, 07:21

... coloring of H l . • If c(w  )=c(w + ) = c(w ⊕ ), then c can be extended to exactly l different proper colorings of H l . The number of vertices of H l does not exceed 3+2log 2 l. Proof: The proof ... number of variables and clauses of the formula Φ. In particular, the number of vertices of H is at most 3 · max A 2 +2·|A 2 \ A 1 |·n and the number of its edges is cubic in...

Ngày tải lên: 07/08/2014, 08:20