REVIEW 1 cited by
Matroidal Mixed Eulerian Numbers
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We make a systematic study of matroidal mixed Eulerian numbers which are certain intersection numbers in the matroid Chow ring generalizing the mixed Eulerian numbers introduced by Postnikov. These numbers are shown to be valuative and obey a log-concavity relation. We establish recursion formulas and use them to relate matroidal mixed Eulerian numbers to the characteristic and Tutte polynomials, reproving results of Huh-Katz and Berget-Spink-Tseng. Generalizing Postnikov, we show that these numbers are equal to certain weighted counts of binary trees. Lastly, we study these numbers for perfect matroid designs, proving that they generalize the remixed Eulerian numbers of Nadeau-Tewari.
Forward citations
Cited by 1 Pith paper
-
Mixed Eulerian numbers and beyond
First explicit formula for mixed Eulerian numbers, and proof that matroidal mixed Eulerian numbers determine Derksen's G-invariant.
Discussion (0). Continue with ORCID to comment.