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4 papers · 2 filters
Descent identities, Hessenberg varieties, and the Weil conjectures
Jason Fulman
The Weil Conjectures are applied to the Hessenberg Varieties to obtain interesting information about the combinatorics of descents in the symmetric group. Combining this with eleme…
The combinatorics of biased riffle shuffles
Jason Fulman
This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely…
Probabilistic measures and algorithms arising from the Macdonald symmetric functions
Jason Fulman
The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to t…
The Rogers-Ramanujan Identities, the Finite General Linear Groups, and the Hall-Littlewood Polynomials
Jason Fulman
The Rogers-Ramanujan identities have been studied from the viewpoints of combinatorics, number theory, affine Lie algebras, statistical mechanics, and quantum field theory. This no…