Báo cáo toán học: "Bijection between bigrassmannian permutations maximal below a permutation and its essential set" pps

... 4 Bijection between bigrassmannian permutations maximal below a permutation and its essential set Masato Kobayashi Department of Mathematics, the University of Tennessee, Knoxville, TN 37996, USA kobayashi@math.utk.edu Submitted: ... observation for essential sets of arbitrary permutations. Our main theorem says that there exists a bijection between bigrassmanian p...

Ngày tải lên: 08/08/2014, 11:20

... Lothaire. — Combinatorics on words. — Reading, Addison-Wesley,  (Encyclop edia of Math. and its Appl., 17). [Mac13] MacMahon (Percy Alexander). — The indices of permutations and the derivation ... paraˆıtre dans J. of Computational and Applied Math., . [GaRa90] George Gasper and Mizan Rahman. — Basic Hypergeometric Series. — London, Cambridge Univ. Press,  (Encyclop ed...

Ngày tải lên: 07/08/2014, 06:22

... σ (i) (b 1 ) and σ (i) decreases in the remaining bricks, and 3. the labels on cells 1 and 3 are x, the label on cell 2 is 1, and the remaining labels are as befor e. We can accomplish this by replacing ... Hook Tableau of shape (4,5,6,6)/(1,3,3) and type (2,2,4,6) A Transposed Special Rim Hook Tableau of shape (4,5,6,6)/(1,3,3) and type (2,3,4,5) Figure 3: A special rim hoo...

Ngày tải lên: 08/08/2014, 12:22

... should mimic that of a regular grammar in that each variable will be multiplied by at most one of A, W, and B and always on the same side. We will name our variables F i and use right multiplication in ... to a bipartition of N 2 . In this section, we use their Pattern Algebra to obtain a q-analog of Kitaev’s [25] Theorem 30 and to deduce a better generating function for per...

Ngày tải lên: 08/08/2014, 12:22

... tableau is actually a standard tableau, and approaches 0 if µ has fewer than k cells. 1 Introduction Let µ be a partition of k,andT a standard Young tableau of shape µ.WesaythatT is a subtableau ... the walk and the chamber. This is the same as the asymp- totic for Brownian motion (appropriately normalized so that the random walk and the Brownian motion have the same variance) s...

Ngày tải lên: 07/08/2014, 08:22

... 1 and Minimum Distance 2 Joanne L. Hall School of Mathematical and Geospatial Sciences Royal Melbourne Institute of Technology joanne.hall@rmit.edu.au Department of Mathematics Australian National ... to find an upper bound on the size of a ball of radius 1 around a code of length 3 and minimum distance 2. OQW-associated graphs and non-extendable partial Latin squares are used to c...

Ngày tải lên: 07/08/2014, 15:23

... (or 321-hexagon-avo- iding) permutations as a class in S n whose Kazhdan-Lusztig and Poincar´e polynomials, and the singular loci of whose Schubert varieties have fairly simple formulas and descrip- tions. ... the case of permutations avoiding a single pattern has attracted much attention (for example, see [BaWe, BWX, S, SW2]), the case of multiple pattern avoidance remains less...

Ngày tải lên: 07/08/2014, 07:21

... [CGHK78] to enumerate permutations avoiding all pairs of a pattern of length 3 and a pattern of length 4. Recently, Albert et al. [AAA + 03] enumerated {1324, 31524}-avoiding permuta- tions, while ... rules and generating trees. They were introduced in [CGHK78] for the study of Baxter permutations and further applied to the study of pattern-avoiding permutations by Stankova a...

Ngày tải lên: 07/08/2014, 07:21

... is an inversion of a permutation σ, then there must be a descent a and a dip b with i ≤ a& lt;jand σ(i) ≥ σ(b) >σ(j), so in fact all Grassmannian permutations and all monodipic permutations are ... Equation (4). • The statistics Mnt and Sink are Narayana distributed over Dyck paths, and the statistics Exc and Def are Narayana distributed over the 321-avoiding perm...

Ngày tải lên: 07/08/2014, 07:21