Báo cáo toán học: "A Closer Look at Lattice Points in Rational Simplices" doc

... tc1kc1−14c1,A Closer Look at Lattice Points in Rational Simplices1Matthias Beck2Dept. of Mathematics, Temple UniversityPhiladelphia, PA 19122matthias@math.temple.eduSubmitted: ... ([Eh]) of counting lattice points in dilated rational poly-topes: Given a rational simplex, that is, an n-dimensional polytope with n + 1 rational vertices, weuse its description as the intersection ... of integer points ( lattice points ) in the dilated polytope. It is straightforward that this number in the opendilated polytope ist−1a, whereas in the closure there areta+ 1 integer...

Báo cáo toán học: "A result on operators on $cal C$ [0,1] " docx

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Báo cáo toán học: "A factor of type II_1 with countable fundamental group " doc

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Báo cáo toán học: "A Note on Sparse Random Graphs and Cover Graphs" docx

... the paths of long edges in C between these subpaths are oflength at least χ, else (b) is violated. Hence, again, there are at least two long edges in C in both directions along the cycle. Finally, ... will terminate in at most n/χ steps and in the end there will be noshort quasicycles.We show now that we have created neither long cycles nor long quasicycles. In- deed, by (b), during the edge ... graphs, Publ. Math. Inst.Hungar. Acad. Sci. 5 (1960) 17-61.[7] T.Luczak, The chromatic number of random graphs, Combinatorica 11 (1991)45-54.the electronic journal of combinatorics 7 (2000),...

Báo cáo toán học: "A Reﬁnement of Cayley’s Formula for Trees" doc

... vertices are integers.3. Exponential generating functionsWe assume that the reader is familiar with the combinatorial interpretation of the oper-ations of addition, multiplication, composition, ... generating functions and the objects that they count. Thus in de-riving functional or diﬀerential equations for generating functions we will describe thedecompositions that lead to these equations, ... a c-parking function by an ordered partition, then cutting it after everyempty parking space decomposes it into a concatenation of c ordinary parking functions.Therefore the generating function...

Báo cáo toán học: "A note on palindromic δ-vectors for certain rational polytopes" pdf

... rings.References[BR07] Matthias Beck and Sinai Robins, Computing the continuous discretely, Under-graduate Texts in Mathematics, Springer, New York, 2007, Integer-point enu-meration in polyhedra.[BS07] Matthias ... theorigin lies in the interior of P then P∨is a rational polytope containing the origin, andP = (P∨)∨. We restrict our attention to those P containing the origin for which P∨is a lattice ... Znand so the lattice points in Znlie at integer heights relative tothe electronic journal of combinatorics 15 (2008), #N18 2Hu; i.e. given u∈ Znthere exists some c ∈ Z such that u∈...

Báo cáo toán học: "A note on polynomials and f -factors of graphs" docx

... Colouring Edge Partitions.Journal of Combinatorial Theory B Volume 94, Issue 2 (2005) 237-244[2] Alon, N. Combinatorial Nullstellensatz. Recent trends in combinatorics (Mátraháza,1995). Combin. ... of v in G. Lovász [5] defines an f-factor of G to be a spanning subgraph H of G in which dH(v) ∈ f (v) for all v ∈ V . Using the combinatorial nullstellensatz of Alon[2], we prove that if ... monomial in g is precisely (−1)|E|+1e∈EXe. Bythe combinatorial nullstellensatz, there exists a non-zero x ∈ {0, 1}|E|such that g(x) = 0.This implies that the first term in g is not zero at...

Báo cáo toán học: "A note on the component structure in random intersection graphs with tunable clustering" pptx

... zero.Let A(v) be the event that the exploration process, initiated at v, at step k+has notterminated and that it at that step has identiﬁed fewer than (µ−1)k+/2 vertices that havenot yet been visited, ... of the lemma by letting C = min{C, C}.Proof of Theorem 2(i). The process of exploring vertices that was brieﬂy described in thebeginning of Section 4, implies that X1, the number of ... will prove that the probability that theexploration process terminates after k steps or that A(v) holds for some v, tends to zero.Note that {|C(v)| = k} ⊆ B(v) for each k, and in particular...

Báo cáo toán học: "A stability property for coeﬃcients in Kronecker products of complex Sn characters" ppsx

... group. Representations, combinatorial algorithms andsymmetric functions”. Second ed. Graduate Texts in Mathematics 203. Springer Ver-lag, 2001.the electronic journal of combinatorics 16 (2009), ... Satz 1 in [4], Theorem 1.6 in [5] or Theorem 2.1 in [9].the electronic journal of combinatorics 16 (2009), #N22 5[12] R.P. Stanley, “Enumerative Combinatorics, Vol. 2” , Cambridge Studies in ... ν) when ℓ(λ) = ℓ(µ)ℓ(ν). In particular, we give, in this case, a new vanishing condition. Finally, in Section 5 we givean application of the main theorem.2 Partitions In this section we recall...

Báo cáo khoa học: "A Study on Automatically Extracted Keywords in Text Categorization" doc

... split, containing 9 603 documents fortraining and 3 299 documents in the ﬁxed test set,and the 90 categories that are present in both train-ing and test sets.As a ﬁrst pre-processing step, ... the 20th International Conference onComputational Linguistics (COLING 2004), pages487–493.Yiming Yang and Xin Liu. 1999. A re-examinationof text categorization methods. In Proceedings ofthe ... occurring three or more times in the training data were selected, with the featurevalue tf*idf. Assuming that extracted keywordsconvey information about a document’s gist, thefeature values in...

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