We study basis partitions, introduced by Hansraj Gupta in 1978. For this family of partitions, we give a recurrence, a generating function, identities relating basis partitions to...
Jennifer M. Nolan, Carla D. Savage, Herbert S. Wil...
Every partition has, for some d, a Durfee square of side d. Every partition with Durfee square of side d gives rise to a "successive rank vector" r = (r1,
: Each linear program (LP) has an optimal basis. The space of linear programs can be partitioned according to these bases, so called the basis partition. Discovering the structures...
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative ...