Báo cáo toán học: "The Insertion Encoding of Permutations" pot

... the operation of Del k when applied to the insertion encoding of π are precisely the insertion encodings of all the permutations σ with σ  π. The proof of this lemma consists of an explicit, ... correspond to insertions of any type provided only that they can be followed by further insertions leading to an element of L. The number of elements of L of length n is the...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 10:20

... eρ + ,andeρ + ∈ E; (ii) λ + e =(λe) + . Proof. (i) Since we assume that the set of all idempotents E of the semigroup S forms a semilattice, all idempotents of S commute. Hence, λ + e =(λe) + e = ... set P (S) of all right translations) of the semigroup S forms a semigroup under the composition of mappings. By the translational hull of S, we mean a subsemigroup Ω(S) consisting...

Ngày tải lên: 06/08/2014, 05:20

... general- ization of [7], of (A(n, d, μ, q)) ∗cop . Our main result is to give the structure of projective modules of D(Γ n,d ). By this, we give the Ext-quiver (with relations) of D (Γ n,d )andshowthatD(Γ n,d ) ... > − −1, the elements X s K u,j and X s  F u,j are linearly independent. Proof. The proof of this lemma is same to the proof of Lemma 2.18 in [7]. For completeness...

Ngày tải lên: 06/08/2014, 05:20

... independence number of general graphs of a given odd girth. We shall prove some similar bounds to those we prove for regular graphs in terms of a measure of the concentration of edges. Monien and ... for the independence number in terms of the odd girth, but instead of the average degree of the graph we have to use another measure of the concentration of edges. 8 Reference...

Ngày tải lên: 07/08/2014, 06:20

... cycles. Let ¯ d be the average degree of vertices of G.Then α(G) ≥  n ¯ d/2. Proof. Since G contains no 3 or 5 cycles, we have α(G) ≥ d 1 (v) (consider the neighbors of v)andα(G) ≥ 1+d 2 (v) (consider ... 2 − ( k−1 k ) n k−1 k d 1 k . Proof. Immediate from Theorem 3. This improves Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, Th...

Ngày tải lên: 07/08/2014, 06:20

... values of n, we shall use elementary estimates and some well-known bounds for ordinary partitions (of a number) to express most values of b n in terms of the number of ordinary partitions of k ... the number of partitions of (the number) n,andQis its ordinary generating function. Also, define p(n, k) to be the number of partitions of n with largest part at most k. We will ha...

Ngày tải lên: 07/08/2014, 06:20