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On p, qbinomial coefficients
 Integers 8 (2008) #A29
"... Abstract In this paper, we develop the theory of a p, qanalogue of the binomial coefficients. Some properties and identities parallel to those of the usual and qbinomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal genera ..."
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Cited by 2 (1 self)
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in combinatorics. Furthermore, several interesting special cases will be disclosed which are analogous to some established identities of the usual binomial coefficients.
Strict unimodality of qbinomial coefficients
, 2013
"... We prove strict unimodality of the qbinomial 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. ..."
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Cited by 9 (5 self)
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We prove strict unimodality of the qbinomial 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.
SOME COMBINATORICS OF BINOMIAL COEFFICIENTS AND THE BLOCHGIESEKER PROPERTY FOR SOME HOMOGENEOUS BUNDLES
, 2001
"... Abstract. A vector bundle has the BlochGieseker property if all its Chern classes are numerically positive. In this paper we show that the nonample bundle pPn (p+ 1) has the BlochGieseker property, except for two cases, in which the top Chern classes are trivial and the other Chern classes are p ..."
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Abstract. A vector bundle has the BlochGieseker property if all its Chern classes are numerically positive. In this paper we show that the nonample bundle pPn (p+ 1) has the BlochGieseker 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 coecient of tk in the rational function (1+t) (np)(1+3t)( n
Combinatorics of binomial primary decomposition
, 2008
"... 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 characteristicfree combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely ..."
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Cited by 15 (6 self)
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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 characteristicfree combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely
Binomial coefficients ()
, 2006
"... 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 DeMoivreLaplace approximation, which has essentially local character and is good only for n ≈ a ..."
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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 DeMoivreLaplace approximation, which has essentially local character and is good only for n ≈ a
Binomial coefficients ()
, 2006
"... 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 prov ..."
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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
Some combinatorics related to central binomial coefficients: GrandDyck paths, coloured noncrossing . . .
, 2008
"... ..."
NEW CONGRUENCES FOR CENTRAL BINOMIAL COEFFICIENTS
 ADV. IN APPL. MATH. 45(2010), NO. 1, 125–148.
, 2010
"... 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 ..."
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Cited by 74 (57 self)
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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
Projective geometry over F1 and the Gaussian binomial coefficients
 Amer. Math. Monthly
"... 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, as the s ..."
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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
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