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Ferrers graphs, D-permutations, and surjective staircases
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2023 (English)In: The Ramanujan journal, ISSN 1382-4090, E-ISSN 1572-9303, Vol. 60, no 2, p. 391-426Article in journal (Refereed) Published
Abstract [en]

We introduce a new family of hyperplane arrangements inspired by the homogenized Linial arrangement (which was recently introduced by Hetyei), and show that the intersection lattices of these arrangements are isomorphic to the bond lattices of Ferrers graphs. Using recent work of Lazar and Wachs we are able to give combinatorial interpretations of the characteristic polynomials of these arrangements in terms of permutation enumeration. For certain infinite families of these hyperplane arrangements, we are able to give generating function formulas for their characteristic polynomials. To do so, we develop a generalization of Dumont’s surjective staircases, and introduce a polynomial which enumerates these generalized surjective staircases according to several statistics. We prove a recurrence for these polynomials and show that in certain special cases this recurrence can be solved explicitly to yield a generating function. We also prove refined versions of several of these results using the theory of complex hyperplane arrangements. 

Place, publisher, year, edition, pages
Springer Nature , 2023. Vol. 60, no 2, p. 391-426
Keywords [en]
Characteristic polynomials, Ferrers graphs, Genocchi numbers, Hyperplane arrangements, Surjective staircases
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-324563DOI: 10.1007/s11139-022-00581-5ISI: 000807283100001Scopus ID: 2-s2.0-85131520663OAI: oai:DiVA.org:kth-324563DiVA, id: diva2:1742106
Note

QC 20230308

Available from: 2023-03-08 Created: 2023-03-08 Last updated: 2023-03-08Bibliographically approved

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Lazar, Alexander

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