On resurgence via asymptotic resurgence

DiPasquale, Michael; Drabkin, Ben

doi:10.48550/arxiv.2003.06980

Cited by 3 publications

(12 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We show that an improved containment exists, albeit asymptotically. As a consequence, we improve an upper bound, given in [7], for the asymptotic resurgence. We write these results in terms of cover ideals of hypergraphs.…”

Section: Introductionmentioning

confidence: 93%

“…We now deal with the case when I (s) i = I s i and ρ(I i ) = 1 for all i. It is to be noted that ρ(I) = 1 need not necessarily imply that I (s) = I s for all s ≥ 1, as you can see in the example given in [7,Remark 5.4]. Theorem 3.9.…”

Section: Resurgence Of a Homogeneous Idealmentioning

confidence: 99%

“…There are no counterexamples to this conjecture yet. For some recent advances in this direction, see [18,17,7].…”

Section: Introductionmentioning

confidence: 99%

“…A more approachable method has been constructed for asymptotic resurgence by DiPasquale, Francisco, Mermin and Schweig in [8]. In [7], DiPasquale and Drabkin studied the resurgence via asymptotic resurgence. They proved that if ρ a (I) < ρ(I), then one can reduce the computation of the resurgence to a finite process.…”

Section: Introductionmentioning

confidence: 99%

“…In [8], DiPasquale et al asked if the resurgence and asymptotic resurgence of edge ideals of graphs are equal. The first counter example was given by Andrew Conner, [7,Example 4.4]. The above theorem gives a class of examples for which the asymptotic resurgence is strictly less than the resurgence.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the resurgence and asymptotic resurgence of homogeneous ideals

Jayanthan¹,

Kumar²,

Mukundan³

2021

Preprint

View full text Add to dashboard Cite

Let K be a field and R = K[x 1 , . . . , x n ]. We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in R. We study the effect on the resurgence when sum, product and intersection of ideals are taken. We obtain sharp upper and lower bounds for the resurgence and asymptotic resurgence of cover ideals of finite simple graphs in terms of associated combinatorial invariants. We also explicitly compute the resurgence and asymptotic resurgence of cover ideals of several classes of graphs. We characterize a graph being bipartite in terms of the resurgence and asymptotic resurgence of edge and cover ideals. We also compute explicitly the resurgence and asymptotic resurgence of edge ideals of some classes of graphs.

show abstract

Section: Introductionmentioning

confidence: 93%

Section: Resurgence Of a Homogeneous Idealmentioning

confidence: 99%

“…There are no counterexamples to this conjecture yet. For some recent advances in this direction, see [18,17,7].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the resurgence and asymptotic resurgence of homogeneous ideals

Jayanthan¹,

Kumar²,

Mukundan³

2021

Preprint

View full text Add to dashboard Cite

show abstract

Cambios en las prácticas culinarias y gastronómicas durante el confinamiento de la COVID-19 en la provincia de Alicante

Tormo-Santamaría

Oltra

Pereto-Rovira

et al. 2021

Rev Esp Nutr Hum Diet

View full text Add to dashboard Cite

Introducción: El confinamiento generado por el estado de alarma decretado a causa de la COVID-19 obligó a la ciudadanía a permanecer en sus casas salvo causa justificada y limitó el acceso a los servicios de restauración colectiva. Estas restricciones supusieron el cambio de hábitos y rutinas de la población, lo que se tradujo en más actividad culinaria en los domicilios. El objetivo del presente estudio es conocer el impacto del confinamiento sobre el comportamiento alimentario estudiando los cambios en las prácticas culinarias y gastronómicas experimentadas por la población alicantina.Material y métodos: Estudio observacional transversal aunque con enfoque diacrónico a partir de la percepción y experiencias de los entrevistados: antes/durante el confinamiento, y muestreo no probabilístico de conveniencia de la población de 18 a 69 años reclutada de forma electrónica entre el 28 de abril y el 10 de mayo de 2020, semanas 7-8 de confinamiento, en la provincia de Alicante (n=679). Análisis estadístico univariable, bivariable y multivariable de los datos mediante el paquete estadístico SPSS. Uso de pruebas no paramétricas al asumir la condición de muestras emparejadas para las respuestas antes (muestra teórica 1) y durante el confinamiento (muestra teórica 2).Resultados: El 70% cocinó con más frecuencia y dedicó más tiempo a hacerlo. Más del 35% amplió sus conocimientos culinarios con un incremento de consulta a la web y redes sociales. Durante el confinamiento predominó la cocina tradicional valenciana y los postres fueron las elaboraciones preferidas. El cocinado en grupo aumentó en más de 11 puntos porcentuales, al igual que comer en compañía, aunque persiste el uso de dispositivos audiovisuales durante el acto de comer. El 84% modificó su percepción sobre algún aspecto relacionado con la alimentación. Las diferencias entre el comportamiento previo a la pandemia y el que se desarrolló durante el confinamiento se han revelado significativas estadísticamente en la mayoría de las variables testadas.Conclusiones: Durante el confinamiento, el aumento de la actividad culinaria se tradujo en una apuesta por la cocina tradicional en detrimento de los platos precocinados, más convivialidad en el acto de comer y un mayor compromiso con el comercio y el consumo de alimentos de proximidad y la sustentabilidad del sistema alimentario.

show abstract

Steiner Configurations ideals: containment and colouring

Ballico¹,

Favacchio²,

Guardo³

et al. 2021

Preprint

View full text Add to dashboard Cite

Given a homogeneous ideal I ⊆ k[x 0 , . . . , xn], the Containment problem studies the relation between symbolic and regular powers of I, that is, it asks for which pair m, r ∈ N, I (m) ⊆ I r holds. In the last years, several conjectures have been posed on this problem, creating an active area of current interests and ongoing investigations. In this paper, we investigated the Stable Harbourne Conjecture and the Stable Harbourne -Huneke Conjecture and we show that they hold for the defining ideal of a Complement of a Steiner configuration of points in P n k . We can also show that the ideal of a Complement of a Steiner Configuration of points has expected resurgence, that is, its resurgence is strictly less than its big height, and it also satisfies Chudnovsky and Demailly's Conjectures. Moreover, given a hypergraph H, we also study the relation between its colourability and the failure of the containment problem for the cover ideal associated to H. We apply these results in the case that H is a Steiner System.

show abstract

On resurgence via asymptotic resurgence

Cited by 3 publications

References 25 publications

On the resurgence and asymptotic resurgence of homogeneous ideals

On the resurgence and asymptotic resurgence of homogeneous ideals

Cambios en las prácticas culinarias y gastronómicas durante el confinamiento de la COVID-19 en la provincia de Alicante

Steiner Configurations ideals: containment and colouring

Contact Info

Product

Resources

About