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- Kyoto UniversityJP2 papers
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5 papers · 1 filter
Asymptotic enumeration of permutations avoiding generalized patterns
Sergi Elizalde
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns al…
Old and young leaves on plane trees
William Y. C. Chen, Emeric Deutsch, Sergi Elizalde
A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees with a given…
The Positive Bergman Complex of an Oriented Matroid
Federico Ardila, Caroline Klivans, Lauren Williams
We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive B…
Subdominant matroid ultrametrics
Federico Ardila
Given a matroid M on the ground set E, the Bergman fan B(M), or space of M-ultrametrics, is a polyhedral complex in R^E which arises in several different areas, such as tropical al…
An Invitation to the Generalized Saturation Conjecture
Anatol N. Kirillov
We report about some results, interesting examples, problems and conjectures revolving around the parabolic Kostant partition functions, the parabolic Kostka polynomials and ``satu…