850 citations
- Indiana University BloomingtonUS8 papers
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- CEA DAM Île-de-FranceFR2 papers
- Centre National de la Recherche ScientifiqueFR2 papers
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4 papers · 1 filter
Counting Dyck paths by area and rank
Saul A. Blanco, T. Kyle Petersen
The set of Dyck paths of length inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the…
Counting maximal antichains and independent sets
Liviu Ilinca, Jeff Kahn
Answering several questions of Duffus, Frankl and Rödl, we give asymptotics for the logarithms of (i) the number of maximal antichains in the n-dimensional Boolean algebra and (ii)…
The interaction of collinear gaps of arbitrary charge in a two dimensional dimer system
Mihai Ciucu
The correlation of gaps in dimer systems was introduced in 1963 by Fisher and Stephenson, who looked at the interaction of two monomers generated by the rigid exclusion of dimers o…
The number of 3-SAT functions
Liviu Ilinca, Jeff Kahn
With the number of functions of boolean variables definable by -SAT formulae, we prove that is asymptotic to . This is a strong form of…