Báo cáo toán học: "Superization and (q, t)-specialization in combinatorial Hopf algebras" pps

... . . . . . . . . . . . . . . . 44 1 Introduction Combinatorial Hopf algebras are special graded and connected Hopf algebras based on certain classes of combinatorial objects. There is no general ... 5: Second and third (q, t)-hook-content formulas of a binary tree: by induction (left diagram) and simplification of the induction (right diagram). Again, it is self-dual as a gra...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

... c 1 to vx and uw, and then colour wy, uy (which is possible since c 1 /∈ L  (uy)), then ux (since the colour of uy is not in its list), then u (since c 1 /∈ L  (u)), and finally uv. In all cases ... Rubin and H. Taylor, Choosability in graphs, in: Proc. West Coast Conference on Combinatorics, Graph Theory and Computing, Arcata, 1979, Congr. Numer. 26 (1980), 125–157. [5] A....

Ngày tải lên: 07/08/2014, 13:21

... Gallai and A. N. Milgra m, Verallgemeinerung eines graphentheoretischen Satzes von R´edei, Acta. Sci. Math. 21 (1960) 181–186. [8] G. Hahn and B. Jackson, A note concerning paths and independence ... vertices in which each pair of vertices forms an edge randomly and independently with probability p = p(n). ∗ Department of Mathematics, Princeton, Princeton, NJ. Email: jacobfox@math.p...

Ngày tải lên: 07/08/2014, 21:21

... described above in Definition 2.3, using the mex operation to fill in increasingly large subarrays containing the seed. Definition 2.6 In algorithm 2, which is well-defined only for principal subarrays A s (p, ... repeat the min calculation. Otherwise, increment k and repeat the process from the beginning (i.e., starting at i = 0), until all entries in A s (p, q) have been filled. Algori...

Ngày tải lên: 08/08/2014, 12:22

... (1.4) tq and (1.5) tq are derived in Section 5 . We conclude the paper by indicating that besides (1.13) each pol ynomial T 2n+1 (t, q) may be given two other combinatorial interpretations involving ... (1 − tq n−1 ) for n ≥ 1 and (t; q) 0 = 1, Jackson [Ja04] (also see [GR90, p. 23]) introduced both q-sine “sin q (u)” and q-cosine “cos q (u)” as being the q-series: sin q (u) :=  n≥...

Ngày tải lên: 08/08/2014, 14:23

... CCs method combined with Windowing and applying new algorithms combating the spectrum overshooting problem and reducing computational complexity. Note that all these modifications and improvements ... developed at Trinity College Dublin, and is a GPP-based rapid prototyping and deployment system. The building blocks of the radio components in a transceiver chain are written in C+...

Ngày tải lên: 20/06/2014, 20:20

... 1)α 4 k · ||u|| ∞ , and the proof is therefore complete. 5 Main result Using the operators N and K in Sections 3 and 4, the nonlinear integral operator Ψ defined in (10) can be expressed in abstract notation ... differentiability, and in fact, f(u, x) is usually in nitely differentiable in most applications. F2 means that the elastic force of the elastic foundation, represente...

Ngày tải lên: 20/06/2014, 20:20

... lower solution α and the upper solution β satisfy, respectively, inequalities (7) and (8) and, conversely, if α and β satisfy (7) and (8) then they are lower and upper solutions in the sense of Definition ... maximal and minimal solutions, and the second one establishes the existence of the greatest and the least solutions in a particular case. The concepts of lower and...

Ngày tải lên: 20/06/2014, 20:20