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Over the past twenty years, lecture hall partitions have emerged as fundamental
combinatorial structures, leading to new generalizations and interpretations of classical …

The Eulerian polynomials and derangement polynomials are two well-studied generating
functions that frequently arise in combinatorics, algebra, and geometry. When one makes an …

Recently the authors introduced lecture hall tableaux in their study of multivariate little $ q $-
Jacobi polynomials. In this paper, we enumerate bounded lecture hall tableaux. We show …

Though much is known about ${\bf s} $-lecture hall polytopes, there are still many
unanswered questions. In this paper, we show that ${\bf s} $-lecture hall polytopes satisfy …

In this note, we investigate some of the fundamental algebraic and geometric properties of $
s $-lecture hall simplices and their generalizations. We show that all $ s $-lecture hall order …

Abstract A lattice polytope PP is called reflexive if its dual P^ ∨ P∨ is a lattice polytope. The
property that PP is unimodularly equivalent to P^ ∨ P∨ does not hold in general, and in fact …

In the interest of finding the minimum additive generating set for the set of s s-lecture hall
partitions, we compute the Hilbert bases for the s s-lecture hall cones in certain cases. In …

The box polynomial of a lattice simplex is a variant of the more well-known h∗-polynomial,
where the open fundamental parallelepiped is considered instead of the half-open. Box …

Lecture hall partitions are fundamental combinatorial objects which have been studied
extensively over the past two decades. These objects have produced new results, as well as …