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The normalized depth function of squarefree powers
The depth of squarefree powers of a squarefree monomial ideal is introduced. Let I be a squarefree monomial ideal of the polynomial ring
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Rigorous computation of Maass cusp forms of squarefree level
We derive an algorithm to rigorously compute and verify Maass cusp forms of squarefree level and trivial character. The main tool we use is an...
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Factoring numbers with elliptic curves
In the present paper, we provide a probabilistic polynomial time algorithm that reduces the complete factorization of any squarefree integer n to...
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Lengths and class numbers
There is an interesting interplay between class numbers and lengths. While trying to find a new proof for the problem of the tenth field, I was...
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On k-free numbers over Beatty sequences
We consider k -free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number α > 1 of finite type τ < ∞ and...
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Nonvanishing Betti numbers of edge ideals of weakly chordal graphs
We show that Kimura’s necessary and sufficient condition for the nonvanishingness of multigraded Betti numbers of edge ideals of chordal graphs can...
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Connected domination in graphs and v-numbers of binomial edge ideals
The v-number of a graded ideal is an algebraic invariant introduced by Cooper et al., and originally motivated by problems in algebraic coding...
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Graded Betti Numbers of Balanced Simplicial Complexes
We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for...
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On ternary quadratic forms over the rational numbers
For a ternary quadratic form over the rational numbers, we characterize the set of rational numbers represented by that form over the rational...
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Squarefree Monomial Ideals with Maximal Depth
Let ( R ,m) be a Noetherian local ring and M a finitely generated R-module. We say M has maximal depth if there is an associated prime p of M such that...