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4 papers · 1 filter
Möbius Polynomials of Face Posets of Convex Polytopes
Meena Jagadeesan, Susan Durst
The Möbius polynomial is an invariant of ranked posets, closely related to the Möbius function. In this paper, we study the Möbius polynomial of face posets of convex polytopes. We…
Equivalence Classes of Permutations Modulo Replacements Between 123 and Two-Integer Patterns
Vahid Fazel-Rezai
We explore a new type of replacement of patterns in permutations, suggested by James Propp, that does not preserve the length of permutations. In particular, we focus on replacemen…
Beyond alternating permutations: Pattern avoidance in Young diagrams and tableaux
Nihal Gowravaram, Ravi Jagadeesan
We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particu…
The Refined Lecture Hall Theorem via Abacus Diagrams
Laura Bradford, Meredith Harris, Brant Jones +3
Bousquet-Mélou & Eriksson's lecture hall theorem generalizes Euler's celebrated distinct-odd partition theorem. We present an elementary and transparent proof of a refined version…