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Koszul duality of operads and homology of partition posets
Koszul duality operads homology partition posets
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2015/3/25
We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex Kˉ(r) formed by chains of partitions which starts at the smallest element and ends at the larg...
Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
Instanton partition functions N=2 SU(N) gauge theories general surface operator W-algebra duals
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2011/3/2
We write down an explicit conjecture for the instanton partition functions in 4d N = 2 SU(N) gauge theories in the presence of a certain type of surface operator.
Jucys-Murphy elements for partition algebras
Partition algebras Jucys–Murphy elements central elements presentation
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2010/12/3
An inductive formula is given for a family of elements which are shown to play a role in the partition algebras which is analogous to that played by classical Jucys–Murphy elements in the group algebr...
Growth partition functions for cancellative infinite monoids
Growth partition functions cancellative infinite monoids
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2010/12/15
We introduce the growth partition function Z,G(t)associated with any cancellative infinite monoid with a finite generator system G. It is a power series in t whose coefficients
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Benford's Law For Coefficients of Modular Forms and Partition Functions
Benford's Law Coefficients of Modular Forms Partition Functions
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2010/11/30
Here we prove that Benford’s law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessa...