Báo cáo toán học: "An Ehrhart Series Formula For Reflexive Polytopes" pptx

... 1, and α m , β n ≥ 0. the electronic journal of combinatorics 13 (2006), #N15 4 An Ehrhart Series Formula For Reflexive Polytopes Benjamin Braun Department of Mathematics Washington University, ... x) d+1 denote the rational generating function for this polynomial (as in [7], chapter 4), called the Ehrhart series of P . See [3] for more information regarding Ehrhart theory....

Ngày tải lên: 07/08/2014, 13:21

... straightforward bookkeeping, cf. [KP07, §§5–8]. However, Theorems 5.3 and 6.1 do not seem to extend to a formula for general q or q ij . As can be seen from the proof of Theorem 4.1, the formula  1 I ... height j k can be before some of the steps with starting height i, σ −1 (i) ≤ σ −1 (j k ). For a q-sequence α, denote by ψ(α) the q-sequence we get by performing the switch described...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 05/08/2014, 10:20

... introduce a forbidden descent we must have j ≤ k<m. Hence, x j <x m = y j ,andx i = y i for i ∈{1, ,k}−{j}. Conversely, suppose that x i ≤ y i for all 1 ≤ i ≤ k,andthatx j <y j for some ... criterion, which is valid for all Coxeter groups. 1 Introduction The classical tableau criterion for Bruhat order on S n says that x ≤ y if and only if x i,k ≤ y i,k for all 1 ≤ i ≤ k...

Ngày tải lên: 07/08/2014, 06:20

... the maximum possible size that can be guaranteed for the given values of n and m. We can reformulate Theorem 3 to have fewer variables by explicitly solving for k max . To do this we need two lemmas. ... Also, b(n, r) = max(f(n, r),g(n, r)) when n ≥ 2 and r ≥ 1. (7) 4 Performance Guarantees The following performance guarantee for the greedy matching procedure is the main result of the p...

Ngày tải lên: 07/08/2014, 06:20

... following: Proposition 4 The smallest edge-sharing necklace for an n-gon is a      3-cycle for n ≡ 0 (mod 6) 4-cycle for n ≡ 2, 4 (mod 6) 6-cycle for n ≡ 1, 3, 5 (mod 6). 2.7 Classification of 4-cycle ... 1 f − 1 . Therefore, maximizing f for fixed v is equivalent to minimizing e/(f − 1). In the next subsection we will show that for each n there is a minimum length c min ∈ {3,...

Ngày tải lên: 08/08/2014, 01:20

... particular, χ Z S n (q) = (q − n + 1) n for q  n − 1, χ mod S n (q) = q(q − n) n−1 for q > n, χ ∗ S n (q) = q(q − n) n−1 . As we mentioned, the formula for χ ∗ S n (q) is already known from ... to the first formula of Lemma 3.2, we get F (Γ 0 ) =  S∈F(Γ 0 ) µ 0 (0, S)F ( ( Φ/S)\E 0 ). This is the theorem. Homomorphic Proof of Theorem 4.3. Apply the same F to the second formula...

Ngày tải lên: 08/08/2014, 01:20

... number. • For verbs, generated forms had to match the original form for tense and negation. • For adjectives, generated forms had to match the original form for degree of comparison and negation. • For ... The forms pro- duced by the tool from the lemma of an observed in- flected word form were subjected to several restric- tions: • For nouns, generated forms had to match the origi...

Ngày tải lên: 07/03/2014, 22:20

... Subject Classification: 05D10 Abstract We give two lower bound formulas for multicolored Ramsey numbers. These formu- las improve the bounds for several small multicolored Ramsey numbers. 1. INTRODUCTION In ... INTRODUCTION In this short article we give two new lower bound formulas for edgewise r-colored Ramsey numbers, R(k 1 ,k 2 , ,k r ), r ≥ 3, defined below. Both formulas are derived...

Ngày tải lên: 07/08/2014, 06:23

... probabilistic proof of a formula for the number of Young tableaux of a given shape. Adv. in Math., 31(1):104–109, 1979. [GT96] Adriano M. Garsia and Glenn Tesler. Plethystic formulas for Macdonald q, ... Acknowledgements The author is grateful to Adriano Garsia for pointing out the q, t-analog of the hook formula in [GT96]. This suggested that the recursion for the hook formula...

Ngày tải lên: 07/08/2014, 15:23