arXiv subjects

Bekir Danış

Publications and source records attributed to Bekir Danış.

3 recordsLinked to original sources

arXiv2026

Conclusive Posets and Torsion in First Homology

We show that a finite poset is conclusive in the sense of Cigler, Jerman and Wojciechowski if and only if the first integral homology group of its order complex is either zero or has positive free rank. Building on the poset splitting machinery developed by Cianci and Ottina, we show that posets on $13$ elements with four maximal and four minimal elements do not admit torsion in the first homology, which was the only remaining configuration whose torsion behavior was unknown. Consequently, we obtain that the only inconclusive posets on $13$ elements are the two dual minimal finite models of the real projective plane. We also provide a rank criterion for the vanishing of the first cohomology over a field.

math.CO↗

arXiv2025

General contractions in new type perturbed metric spaces

We focus on the new type perturbed metric spaces and introduce a contraction mapping namely new type perturbed Kannan mappings. For these mappings, we show that Banach's fixed point theorem holds. Moreover, this new generalization of Banach's contraction principle does not depend on the continuity of the operator.

math.GM↗

arXiv2020

Generic initial ideals of modular polynomial invariants

We study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all cases an explicit generating set is known we calculate the generic initial ideal of the Hilbert ideal of a cyclic group of prime order for all monomial orders. We also clarify the Klein four group and note that its Hilbert ideals are Borel fixed with certain orderings of the variables. In all situations we consider, there is a monomial order such that the gin of the Hilbert ideal is equal to its initial ideal. Along the way we show that gin respects a permutation of the variables in the monomial order.

math.AC↗