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09/11/2023
Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy
Describing the equality conditions of the Alexandrov–Fenchel inequality ...
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08/20/2023
Computational complexity of counting coincidences
Can you decide if there is a coincidence in the numbers counting two dif...
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09/13/2022
What is a combinatorial interpretation?
In this survey we discuss the notion of combinatorial interpretation in ...
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07/12/2022
Positivity of the symmetric group characters is as hard as the polynomial time hierarchy
We prove that deciding the vanishing of the character of the symmetric g...
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05/05/2022
Effective poset inequalities
We explore inequalities on linear extensions of posets and make them eff...
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04/27/2022
What is in #P and what is not?
For several classical nonnegative integer functions, we investigate if t...
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10/20/2021
Log-concave poset inequalities
We study combinatorial inequalities for various classes of set systems: ...
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09/22/2020
On the number of contingency tables and the independence heuristic
We obtain sharp asymptotic estimates on the number of n × n contingency ...
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04/02/2019
Combinatorial inequalities
This is an expanded version of the Notices of the AMS column with the sa...
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03/20/2019
Phase transition in random contingency tables with non-uniform margins
For parameters n,δ,B, and C, let X=(X_kℓ) be the random uniform continge...
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05/09/2018
On the number of integer points in translated and expanded polyhedra
We prove that the problem of minimizing the number of integer points inp...
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05/09/2018
Presburger Arithmetic with algebraic scalar multiplications
We study complexity of integer sentences in S_α = (R, <, +,Z, x α x), wh...
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03/18/2018
Complexity problems in enumerative combinatorics
We give a broad survey of recent results in Enumerative Combinatorics an...
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10/11/2017
VC-dimension of short Presburger formulas
We study VC-dimension of short formulas in Presburger Arithmetic, define...
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08/28/2017