1 citations · 1 across the 11 of their papers we have counts for
12 papers
Field independence of the first seven Betti numbers of flag complexes
Omkar Javadekar
In 2006, Katzman showed that the first six Betti numbers of the Stanley--Reisner ring of a flag complex are field independent. He also found flag complexes on eleven vertices whose…
The Betti numbers and Golodness of numerical semigroup rings of Sally type
Manav Batavia, Omkar Javadekar, Manohar Kumar
We determine explicit formulae for the Betti numbers of the defining toric ideals of two families of numerical semigroups of Sally type, resolving and extending beyond several conj…
On the weak Lefschetz property of Artinian Gorenstein algebras of codimension three in arbitrary characteristic
Omkar Javadekar
Let be a field, , and be a standard graded Artinian Gorenstein -algebra of codimension three. The -vector of such an algebra i…
Purity of extremal rays of Betti cones
H. Ananthnarayan, Omkar Javadekar, Rajiv Kumar
Let be a standard graded algebra over an infinite field , and let and denote the rational c…
On licci squarefree monomial ideals
Om Prakash Bhardwaj, Trung Chau, Omkar Javadekar
We study the licci property for several classes of squarefree monomial ideals arising from graphs and related combinatorial structures. We characterize licci bi-Cohen-Macaulay squa…
On Golod Subdeterminantal Ideals
Omkar Javadekar
Let be a matrix of indeterminates and let be a polynomial ring over an infinite field $\mathbb{k}…
Projective monomial curves associated to numerical semigroups with multiplicity , width , and embedding dimension
Om Prakash Bhardwaj, Trung Chau, Omkar Javadekar
Numerical semigroups with multiplicity , width , and embedding dimension are of the form $$S(e,m,n) = \langle \{e, e+1, \ldots, 2e-1\} \setminus \{e+m, e+n\} \rangle,…
A comparison of the regularity of certain classes of monomial ideals and their integral closures
Omkar Javadekar
Let , be an ideal of , and denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal…
Extremal behavior of ideals of minors
Trung Chau, Michael DeBellevue, Souvik Dey +2
Let be either a fiber product or an artinian stretched Gorenstein ring, with in the latter case. We prove that the…
Betti cones over fibre products
H. Ananthnarayan, Omkar Javadekar, Rajiv Kumar
Let be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded -modules. As an application of this, we show…
Linear quotients of connected ideals of graphs
H. Ananthnarayan, Omkar Javadekar, Aryaman Maithani
As a higher analogue of the edge ideal of a graph, we study the -connected ideal . This is the monomial ideal generated by the connected subsets of size $t…
Syzygies of associated graded modules
H. Ananthnarayan, Manav Batavia, Omkar Javadekar
Given a finitely generated module over a Noetherian local ring , we give a characterization for the first syzygy of the associated graded module to be…