共查询到20条相似文献,搜索用时 31 毫秒
1.
Zach Teitler 《Proceedings of the American Mathematical Society》2008,136(5):1575-1579
In 2006, M. Mustaţă used jet schemes to compute the multiplier ideals of reduced hyperplane arrangements. We give a simpler proof using a log resolution and generalize to non-reduced arrangements. By applying the idea of wonderful models introduced by De Concini-Procesi in 1995, we also simplify the result. Indeed, Mustaţă's result expresses the multiplier ideal as an intersection, and our result uses (generally) fewer terms in the intersection.
2.
Reiho Sakamoto 《Journal of Algebraic Combinatorics》2008,27(1):55-98
In proving the Fermionic formulae, a combinatorial bijection called the Kerov–Kirillov–Reshetikhin (KKR) bijection plays the
central role. It is a bijection between the set of highest paths and the set of rigged configurations. In this paper, we give
a proof of crystal theoretic reformulation of the KKR bijection. It is the main claim of Part I written by A. Kuniba, M. Okado,
T. Takagi, Y. Yamada, and the author. The proof is given by introducing a structure of affine combinatorial R matrices on rigged configurations. 相似文献
3.
Manuel González Villa 《Mathematische Zeitschrift》2013,274(3-4):1113-1118
4.
We find a combinatorial setting for the coefficients of the Boros–Moll polynomials P
m
(a) in terms of partially 2-colored permutations. Using this model, we give a combinatorial proof of a recurrence relation on
the coefficients of P
m
(a). This approach enables us to give a combinatorial interpretation of the log-concavity of P
m
(a) which was conjectured by Moll and confirmed by Kauers and Paule. 相似文献
5.
Mark Wildon 《The Ramanujan Journal》2008,17(3):355-367
In 2003, Maróti showed that one could use the machinery of ℓ-cores and ℓ-quotients of partitions to establish lower bounds for p(n), the number of partitions of n. In this paper we explore these ideas in the case ℓ=2, using them to give a largely combinatorial proof of an effective upper bound on p(n), and to prove asymptotic formulae for the number of self-conjugate partitions, and the number of partitions with distinct
parts. In a further application we give a combinatorial proof of an identity originally due to Gauss.
Dedicated to the memory of Dr. Manfred Schocker (1970–2006) 相似文献
6.
Günter M. Ziegler 《Inventiones Mathematicae》2002,147(3):671-691
The Kneser conjecture (1955) was proved by Lovász (1978) using the Borsuk-Ulam theorem; all subsequent proofs, extensions
and generalizations also relied on Algebraic Topology results, namely the Borsuk-Ulam theorem and its extensions. Only in
2000, Matoušek provided the first combinatorial proof of the Kneser conjecture. Here we provide a hypergraph coloring theorem,
with a combinatorial proof, which has as special cases the Kneser conjecture as well as its extensions and generalization
by (hyper)graph coloring theorems of Dol’nikov, Alon-Frankl-Lovász, Sarkaria, and Kriz. We also give a combinatorial proof
of Schrijver’s theorem.
Oblatum 17-IV-2001 & 12-IX-2001?Published online: 19 November 2001
An erratum to this article is available at . 相似文献
7.
In a paper from 1954 Marstrand proved that if K ⊂ ℝ2 is a Borel set with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure
for almost-all directions. In this article, we give a combinatorial proof of this theorem, extending the techniques developed
in our previous paper [9]. 相似文献
8.
Alberto Del Pia 《4OR: A Quarterly Journal of Operations Research》2010,8(1):105-108
We survey the main results of the PhD Thesis presented by the author in January 2009 at the University of Padova. This work
was supervised by Giacomo Zambelli. The thesis is written in English and is available from the author upon request. In this
work we consider the Edmonds–Johnson property and we survey some related results. Next we present our contributions, that
consist into two classes of matrices with the Edmonds–Johnson property. Our work generalizes previous results by Edmonds and
Johnson (Math Program 5:88–124, 1973), and by Conforti et al. (in Integer programming and combinatorial optimization, proceedings
of IPCO 2007). Both our results are special cases of a conjecture introduced by Gerards and Schrijver. 相似文献
9.
Mathias Lederer 《Annals of Combinatorics》2006,10(3):389-394
From Kostant’s multiplicity formula for general linear groups, one can derive a formula for the Kostka numbers. In this note
we give a combinatorial proof of this formula.
Received January 7, 2005 相似文献
10.
Andrews gave a combinatorial proof of the Rogers–Fine identity. In this paper, we present a combinatorial proof of a special
case of Watson’s 8
φ
7 transformation formula, which is a generalization of Andrews’ proof.
A.J. Yee is an Alfred P. Sloan Research Fellow. 相似文献
11.
In this paper, we first give a direct construction of the ℕ-measure of a continuous state branching process. Then we prove,
with the help of this ℕ-measure, that any continuous state branching process with immigration can be constructed as the independent
sum of a continuous state branching process (without immigration), and two immigration parts (jump immigration and continuum
immigration). As an application of this construction of a continuous state branching process with immigration, we give a proof
of a necessary and sufficient condition, first stated without proof by M. A. Pinsky [Bull. Amer. Math. Soc., 1972, 78: 242–244],
for a continuous state branching process with immigration to a proper almost sure limit. As another application of the ℕ-measure,
we give a “conceptual” proof of an L log L criterion for a continuous state branching process without immigration to have an L
1-limit first proved by D. R. Grey [J. Appl. Prob., 1974, 11: 669–677]. 相似文献
12.
In this note we study the local behaviour of the multi-variate Bernstein polynomials B, on the d-dimensional simplex S⊂R
d. For function f admitting derivatives of sufficient high order in x∈S we derive the complete asymptotic expansion of Bnf as n tends to infinity. All the coefficients of n−1 that only depend on f and x are calculated explicitly. It turns out that combinatorial numbers play an important role. Par
result generalize recent formulae due to R. Zhang in a way. 相似文献
13.
Annals of Combinatorics - The Murnaghan–Nakayama rule is a combinatorial rule for the character values of symmetric groups. We give a new combinatorial proof by explicitly finding the trace... 相似文献
14.
Thomas J. Haines 《manuscripta mathematica》2000,101(2):167-174
We consider the matrix for the Satake isomorphism with respect to natural bases. We give a simple proof in the case of Chevalley
groups that the matrix coefficients which are not obviously zero are in fact positive numbers. We also relate the matrix coefficients
to Kazhdan–Lusztig polynomials and to Bernstein functions.
Received: 29 June 1999 / Revised version: 7 September 1999 相似文献
15.
Annals of Combinatorics - In work with A. Yong, the author introduced genomic tableaux to prove the first positive combinatorial rule for the Littlewood–Richardson coefficients in... 相似文献
16.
We consider an operator of Bernstein for symmetric functions and give an explicit formula for its action on an arbitrary Schur
function. This formula is given in a remarkably simple form when written in terms of some notation based on the code of a
partition. As an application, we give a new and very simple proof of a classical result for the KP hierarchy, which involves
the Plücker relations for Schur function coefficients in a τ-function for the hierarchy. This proof is especially compact because we are able to restate the Plücker relations in a form
that is symmetrical in terms of partition code notation. 相似文献
17.
Guy David 《Journal of Geometric Analysis》2010,20(4):837-954
We give a new proof and a partial generalization of Jean Taylor’s result (Ann. Math. (2) 103(3), 489–539, 1976) that says that Almgren almost-minimal sets of dimension 2 in ℝ3 are locally C
1+α
-equivalent to minimal cones. The proof is rather elementary, but uses a local separation result proved in Ann. Fac. Sci.
Toulouse 18(1), 65–246, 2009 and an extension of Reifenberg’s parameterization theorem (David et al. in Geom. Funct. Anal. 18, 1168–1235, 2008). The key idea is still that if X is the cone over an arc of small Lipschitz graph in the unit sphere, but X is not contained in a disk, we can use the graph of a harmonic function to deform X and substantially diminish its area. The local separation result is used to reduce to unions of cones over arcs of Lipschitz
graphs. A good part of the proof extends to minimal sets of dimension 2 in ℝ
n
, but in this setting our final regularity result on E may depend on the list of minimal cones obtained as blow-up limits of E at a point. 相似文献
18.
Axel Hultman 《Journal of Combinatorial Theory, Series A》2009,116(3):564-580
We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w∈Sn is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups.A byproduct of this result and its proof is a set of inequalities relating Betti numbers of complexified inversion arrangements to Betti numbers of closed Schubert cells. Another consequence is a simple combinatorial interpretation of the chromatic polynomial of the inversion graph of a permutation which avoids the above patterns. 相似文献
19.
Toda (in SIAM J. Comput. 20(5):865–877, 1991) proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P
#P
, namely the class of languages that can be decided by a Turing machine in polynomial time given access to an oracle with
the power to compute a function in the counting complexity class #P. This result, which illustrates the power of counting, is considered to be a seminal result in computational complexity theory.
An analogous result in the complexity theory over the reals (in the sense of Blum–Shub–Smale real machines in Bull. Am. Math. Soc. (NS) 21(1): 1–46, 1989) has been missing so far. In this paper we formulate and prove a real analogue of Toda’s theorem. Unlike Toda’s proof in
the discrete case, which relied on sophisticated combinatorial arguments, our proof is topological in nature. As a consequence
of our techniques, we are also able to relate the computational hardness of two extremely well-studied problems in algorithmic
semi-algebraic geometry: the problem of deciding sentences in the first-order theory of the reals with a constant number of
quantifier alternations, and that of computing Betti numbers of semi-algebraic sets. We obtain a polynomial time reduction
of the compact version of the first problem to the second. This latter result may be of independent interest to researchers
in algorithmic semi-algebraic geometry. 相似文献
20.
J. Korevaar 《Combinatorica》2001,21(2):239-250
Dedicated to the memory of Paul Erdős
In connection with the elementary proof of the prime number theorem, Erdős obtained a striking quadratic Tauberian theorem
for sequences. Somewhat later, Siegel indicated in a letter how a powerful "fundamental relation" could be used to simplify
the difficult combinatorial proof. Here the author presents his version of the (unpublished) Erdős–Siegel proof. Related Tauberian
results by the author are described.
Received December 20, 1999 相似文献