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

... t c 1  k c 1  − 1 4c 1 , A Closer Look at Lattice Points in Rational Simplices 1 Matthias Beck 2 Dept. of Mathematics, Temple University Philadelphia, PA 19122 matthias@math.temple.edu Submitted: ... ([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, we us...

Ngày tải lên: 07/08/2014, 06:20

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Ngày tải lên: 05/08/2014, 10:20

... the paths of long edges in C between these subpaths are of length 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 no short quasicycles. We show now that we have created neither long cycles nor long quasicycles. In- deed, b...

Ngày tải lên: 07/08/2014, 06:20

... vertices are integers. 3. Exponential generating functions We 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 the decompositions that lead to these equ...

Ngày tải lên: 07/08/2014, 08:22

... 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 ... the origin lies in the interior of P then P ∨ is a rational polytope containing the origin, and P = (P ∨ ) ∨ . We restrict our attention to those P containing the orig...

Ngày tải lên: 07/08/2014, 15:22

... Colouring Edge Partitions. Journal of Combinatorial Theory B Volume 94, Issue 2 (2005) 237-244 [2] Alon, N. Combinatorial Nullstellensatz. Recent trends in combinatorics (M´atrah´aza, 1995). Combin. ... of v in G. Lov´asz [5] defines an f-factor of G to be a spanning subgraph H of G in which d H (v) ∈ f (v) for all v ∈ V . Using the combinatorial nullstellensatz of Alon [2], we prove tha...

Ngày tải lên: 07/08/2014, 15:22

... zero. Let A(v) be the event that the exploration process, initiated at v, at step k + has not terminated and that it at that step has identified fewer than (µ−1)k + /2 vertices that have not 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 the beginning of Section 4, implies that X...

Ngày tải lên: 07/08/2014, 15:23

... group. Representations, combinatorial algorithms and symmetric 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 Stud...

Ngày tải lên: 07/08/2014, 21:21

... split, containing 9 603 documents for training 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 on Computational Linguistics (COLING 2004), pages 487–493. Yiming Yang and Xin Liu. 1999. A re-examination of text categorization methods. In Proceedings of t...

Ngày tải lên: 08/03/2014, 02:21