Abstract not found

in combinatorics. Furthermore, several interesting special cases will be disclosed which are analogous to some established identities of the usual binomial coefficients.

We prove strict unimodality of the q-binomial coefficients () n as polynomials in q. k q The proof is based on the combinatorics of certain Young tableaux and the semigroup property of Kronecker coefficients of Sn representations.

Abstract. A vector bundle has the Bloch-Gieseker property if all its Chern classes are numerically positive. In this paper we show that the non-ample bun-dle pPn (p+ 1) has the Bloch-Gieseker property, except for two cases, in which the top Chern classes are trivial and the other Chern classes are positive. Our method is to reduce the problem to showing, e.g. the positivity of the coe-cient of tk in the rational function (1+t) (np)(1+3t)( n

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely

ABSTRACT. The sequence n ↦ → () a n of real binomial coefficients is studied in two main cases: a ≫ n and n ≫ a. In the first case a uniform approximation with high accuracy is obtained, in contrast to DeMoivre-Laplace approximation, which has essentially local character and is good only for n ≈ a

Abstract. We prove that if the signed binomial coefficient (−1) i`k ´ viewed i modulo p is a periodic function of i with period h in the range 0 ≤ i ≤ k, then k + 1 is a power of p, provided h is prime to p and not too large compared to k. (In particular, 2h ≤ k suffices.) As an application, we

Abstract not found

Let p be a prime and let a be a positive integer. In this paper we determine ∑p a −1 2k k=0 /mk p−1

notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and algebra, but it is rarely discussed as such. The purpose of this article is to bring it to the attention of a broader audience