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» On the span of polynomials with integer coefficients
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DM
2002
93views more  DM 2002»
13 years 5 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»
13 years 5 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
13 years 3 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»
13 years 5 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»
13 years 12 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...