Báo cáo toán học: "SIGNED WORDS AND PERMUTATIONS, II; THE EULER-MAHONIAN POLYNOMIALS" doc

... record values and the length function. Two approaches are here systematically explored, us- ing the flag-major index on the one hand, and the flag-inversion number on the other hand. The MacMahon ... using the “fmaj” interpretation, on the one hand, and the “finv” geometry, on the other. In each case we will go beyond the three-variable case, as we consider the gene...

Ngày tải lên: 07/08/2014, 08:22

... corresponding rows of B 1 and B 2 by placing the brick with the ∗ at the end of the row, and (3) order the rows of B 1 and B 2 of the same size by ensuring that the smallest elements in the corresponding ... µ-brick starts at the cell and a λ-brick does not, and record an N if neither a λ-brick nor a µ-brick starts at the cell. We then define the word of the c...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:20

... of the numbering of the vertices of K or the choices of α ij . As is often the case with algebraic shifting, we do not use the definition directly, but rather some theorems that characterize the ... ···<s j } and T = {t 1 < ···<t j } are j-subsets of integers, then: • S ≤ P T under the standard partial order if s p ≤ t p for all p ;and • S< L T under the lexicogr...

Ngày tải lên: 07/08/2014, 06:20

... for any p either 2p or −2p is covered by A 1 3 , and the other element of the pair {2p, −2p} belongs to one of the sets R a 5 (a 5 =1, 2, 3, 4),  a 5 R a 5 = P , and, therefore, there exists ... = 1 n . Then the result follows from Theorem 4.7. Theorem 4.7 provides a basis for a stronger and more general result ob- tained in [8]. 5OpenProblems The concepts of stapled sequences...

Ngày tải lên: 07/08/2014, 06:20

... nondecreasing. The subgraph of G consisting of P i and P j and the chords joining them has this form. Process the chords in H in the order L. If the next chord shares an endpoint with the current ... other path, then the second chord among these two is assigned to the other path. Hence the chords assigned to each path have distinct endpoints on the other path. Bound 2:...

Ngày tải lên: 07/08/2014, 21:20

... optical properties. The largest standard deviation occurred in the green and the far red domain where the reflectance and the transmittance were relatively the highest. This means that variability of the transmittance ... was found in the upper part of the tree. A vertical gradient of the mean transmittance existed from the bottom to the top of the tree crown. Li...

Ngày tải lên: 08/08/2014, 14:22

... question. Acknowledgments. The authors are grateful to the referees for the careful reading of the manuscript and to M. Atkinson for his remarks. The final version of the paper was written during the first author’s ... for the cases k =2, 3, 4 by using generating trees, the symmetries in the set of the P k ,and the structure of the 321-avoiding permutations via Sch...

Ngày tải lên: 07/08/2014, 07:21

... define the base trapezoid as the region surrounded by the x-axis, the last up step that touches the x-axis, then the necessary number of horizontal steps to reach the last down step, and finally the ... involves a labelling of the cells in the region of a Motzkin path. The region of a Motzkin path is meant to be the area surrounded by the path and the x-axis. Fur...

Ngày tải lên: 07/08/2014, 07:21

... edges, all at the same height. Let t be the position of the first floating step after the long vertical edge (the first excedance, and the only dip) and u the position of the floating step of the long ... B’s of the string, starting with 1 at the rightmost B, moving to the left and increasing with one at each successive B; • add the next label to the left of the...

Ngày tải lên: 07/08/2014, 07:21