Báo cáo toán học: "Promotion and evacuation on standard Young tableaux of rectangle and staircase shape" doc

... representation-theoretical in-terpretation.the electronic journal of combinatorics 18 (2011), #P18 15Promotion and evacuation on standard Young tableaux of rectangle and staircase shapeSteven Pon∗Department ... position of n in ǫ∗◦ ∂(T ) is the same as the position of n in T (because the sliding in the action of promotion and the ﬁrst application of dual-sliding in the deﬁnition of dual -evacuation will ... Rhoades on rectangular tableaux, can help todemonstrate the cyclic sieving phenomenon of promotion action on SY T (sck).1 IntroductionPromotion and evacuation (denoted here by ∂ and ǫ, respectively...

Báo cáo toán học: " Could petroleum biodegradation be a joint achievement of aerobic and anaerobic microrganisms in deep sea reservoirs?" pptx

... vortex and adding lisozyme to a final concentration of 17 mg/mL. After incubation at 37 ºC for 1 h, proteinase K and SDS were added (final concentration of 0.7 mg/mL and 2 %, respectively) and ... preparation and incubation of the anaerobic and mixed microorganism consortium. Each consortium biodegradation experiment was composed of 40 mL of Zinder nutrient medium (Zinder et al., 1984) containing ... absent 6consortia and the biodegradation processes were stimulated by adsorbing oil on sterilized sand. The experiments were carried out in duplicate and controls of consortia and Zinder medium...

Báo cáo toán học: "An improved bound on the minimal number of edges in color-critical graphs" pot

... second ingredient of our proof is the following result of Stiebitz.Lemma 3 ([5]) Let G be a k-critical graph containing at least one vertex of degree k − 1.Then the number of connected components ... electronic journal of combinatorics 1 (1998), #R4 3Let r be the number of connected components of H(G), then trivially|E(H(G))|≥nH−r. (2)Also, by Lemma 3, the number of connected components of ... components of its high-vertex subgraph H(G) does not exceedthe number of connected components of its low-vertex subgraph L(G).Proof of Theorem 1. Let L(G) and H(G) be the low-vertex and the high-vertex...

Báo cáo toán học: "A new bound on the domination number of graphs with minimum degree two" docx

... assumptions,if z ∈ N(u) ∪ N(v), then z /∈ X and dG(z) ≥ 3.Let G′= G − {u, v}. Let Gu and Gvbe the components of G′containing u′ and v′, respectively, and let Gwbe the component of ... identifying v1 and v2 and deleting {u1, u2} a type-1 G-reducible graph.the electronic journal of combinatorics 18 (2011), #P12 2Summary of the proof of T heorem 4. We proceed by induction on the ... Xw).Proof. Suppose G′′= Gv. By construction, dGw(x) ≥ 2 for all x ∈ V (Gw) \ Xw, and so δ1(Gw; Xw) = 0. Note that if K is a component of Gw, then K is also a component of G′, and...

Báo cáo toán học: "Conjectured Combinatorial Models for the Hilbert Series of Generalized Diagonal Harmonics Modules" docx

... 1).Deﬁnition 2. Let λ be a partition of N.Letc be one of the N cells in the diagram of λ.the electronic journal of combinatorics 11 (2004), #R68 2Proof. The bijection F is based on the tile insertion ... of notation translation,keeping in mind that the permutation σ corresponds to the reversal of the word of f.5 Univariate Symmetry of CHn,k,m(q, t)This section generalizes the constructions ... previous work of F. Bergeron, A. Garsia, J. Haglund, M. Haiman, G. Tesler,et al. regarding the diagonal harmonics module and its connections to representationtheory, symmetric functions, Macdonald...

Báo cáo toán học: "Promotion and Evacuation" docx

... promotion and evacuation on the maximal chains of Bnare equivalent to “classical” promotion and evacuation on A. The linear extensions of A are just all the permutations w of {1, . . . , n}, and ... representation theory. Both Stembridge and Berenstein-Kirillov deal with semistandard tableaux, while here we consider only the special case of standard tableaux. While standard tableaux have ... ubject Classiﬁcations: 06A07Dedicated to Anders Bj¨orner on the occasion of his sixtieth birthday.AbstractPromotion and evacuation are bijections on the set of linear extensions of a ﬁniteposet...

Báo cáo toán học: "A New Statistic on Linear and Circular r-Mino Arrangements" potx

... F1=1,etc.,andL1=1,L2=3,etc.).Polynomial generalizations of Fn and/ or Lnhave arisen as generating functions forstatistics on binary words [1], lattice paths [4], and linear and circular ... functions for a pair of statistics on linear and circular r-minoarrangements.2Linearr-Mino ArrangementsConsider the problem of ﬁnding the number of ways to place k indistinguishable non-overlapping ... Generalizations of F(r)n and/ or L(r)nhave arisen similarly in connection withstatistics on Morse code sequences [2], [3].In the present paper, we study the polynomial generalizationsF(r)n(q,...

Báo cáo toán học: "A normalization formula for the Jack polynomials in superspace and an identity on partitions" pps

... particular, the cells in a good˜Λ-conﬁguration all lie in the ﬁ rs t m rows of ˜Λ, and thus the concept of good˜Λ-conﬁguration on l y depends on the fe rmionic portion of ˜Λ.We will now see that ... combinatorial and relies on the explicit expression in terms of admissible tableaux of the non-symmetric Jack polynomials. In the ﬁnal step of the proofappears an identity on weighted sums of partitions ... do not belong to˜Λ. Thereforenone of these letters occupies a 0-critical position in T and thus each of them contributesa fa ctor 1 in d0T(α).An easy consequence of the proof of the lemma...

Báo cáo toán học: "Promotion operator on rigged conﬁgurations of type A" potx

... conﬁgurationsA general deﬁnition of rigged conﬁguration of arbitrary types can be found in [14, Section 3.1].Here we are only concerned with type Anrigged conﬁgurations and review their deﬁnition.Given ... pr on RC and conjectured [14, Conjecture 4.12] that prcorresponds to the promotion operator pr under the bijection Φ. Several necessary conditions of promotion operators were established and ... promotion on RC and Φ is an afﬁne crystal isomorphism.Another reformulation of the bijection from tensor products of crystals to rigged conﬁgura-tions in terms of the energy function of afﬁne...

Báo cáo toán học: " Interface modification effect between p-type a-SiC:H and ZnO:Al in p-i-n amorphous silicon solar cells" potx

... Youngkuk Kim1, Jinjoo Park1, and Junsin Yi*1 1School of Information and Communication Engineering, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, 440-746, South Korea 2Photovoltaic ... depth of about 810 nm, because of the smaller energy bandgap of the nanocrystalline silicon, an opposite banding occurs at the valence band. It helps generated holes to move towards the TCO and ... AZO/p-type a-SiC:H and AZO/ p+ a-SiC:H/p-type a-SiC:H front interface and (b) AZO/p-type a-SiC:H and AZO/nc-Si/p-type a-SiC:H front interface. This Provisional PDF corresponds to the article...

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