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» On the span of polynomials with integer coefficients
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DM
2002
93views more  DM 2002»
14 years 11 months ago
A proof of the q, t-Catalan positivity conjecture
We present here a proof that a certain rational function Cn(q, t) which has come to be known as the "q, t-Catalan" is in fact a polynomial with positive integer coeffici...
Adriano M. Garsia, James Haglund
COMBINATORICS
2004
106views more  COMBINATORICS 2004»
14 years 11 months ago
Random Matrices, Magic Squares and Matching Polynomials
Characteristic polynomials of random unitary matrices have been intensively studied in recent years: by number theorists in connection with Riemann zetafunction, and by theoretica...
Persi Diaconis, Alexander Gamburd
MFCS
2010
Springer
14 years 9 months ago
Weights of Exact Threshold Functions
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute va...
László Babai, Kristoffer Arnsfelt Ha...
DM
2008
90views more  DM 2008»
14 years 11 months ago
On sums of binomial coefficients and their applications
In this paper we study recurrences concerning the combinatorial sum n r m = kr (mod m) n k and the alternate sum kr (mod m)(-1)(k-r)/m n k , where m > 0, n 0 and r are integers....
Zhi-Wei Sun
ISAAC
2009
Springer
109views Algorithms» more  ISAAC 2009»
15 years 6 months ago
A Linear Vertex Kernel for Maximum Internal Spanning Tree
We present an algorithm that for any graph G and integer k ≥ 0 in time polynomial in the size of G either nds a spanning tree with at least k internal vertices, or outputs a ne...
Fedor V. Fomin, Serge Gaspers, Saket Saurabh, St&e...