Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen-Macaulayness of the second symbolic power or of all symbolic powers of a Stanley-Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen-Macaulay. In particular, all symbolic powers are Cohen-Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen-Macaulayness can pass from a symbolic power to another symbolic powers in different ways.Comment: The published version of this paper contains a gap in the proofs of Theorem 2.5 and Theorem 3.5. This version corrects the proofs with almost the same arguments. Moreover, we have to modify the definition of tight complexes in Theorem 2.5. These changes don't affect other things in the published version. A corrigendum has been sent to the journa

The Buchsbaum property of symbolic powers of Stanley–Reisner ideals of dimension 1

AbstractLet S be a polynomial ring and I be the Stanley–Reisner ideal of a simplicial complex Δ. The purpose of this paper is investigating the Buchsbaum property of S/I(r) when Δ is pure dimension 1. We shall characterize the Buchsbaumness of S/I(r) in terms of the graphical property of Δ. That is closely related to the characterization of the Cohen–Macaulayness of S/I(r) due to the first author and N.V. Trung

Characterization of graphs whose a small power of their edge ideals has a linear free resolution

Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G)^2$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 3$. Similarly, we show that $I(G)^3$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 4$. We deduce these characterizations from a general formula for the regularity of powers of edge ideals of gap-free graphs $${\rm reg}(I(G)^s) = \max({\rm reg} I(G) + s-1,2s),$$ for $s =2,3$.Comment: 14 pages. Update a proof of Theorem 2.13 with a statement for a squarefree monomial ideal. arXiv admin note: text overlap with arXiv:2109.0639

Vietnamese Culture in the Fashion Industry: The Case of TiredCity and BARO

The international fashion industry has undergone significant development over the years, in response to the change in consumer preferences, technological advancements, globalization, and socio-cultural shifts. Vietnamese fashion has been steadily gaining recognition and prominence in the global fashion industry with cultural identity and unique aesthetics. The combination of traditional elements with modern influences has resulted in a unique and distinct style that is gaining recognition in both domestic and international markets. The influence of Vietnamese culture in the fashion industry is reflected in many aspects such as design, material, and products. The case studies of two distinct brands TiredCity and BARO explore the incorporation of Vietnamese culture in the fashion industry. Both brands aim to celebrate and promote the rich heritage of Vietnamese culture while presenting it in a contemporary and fashion-forward manner. By celebrating Vietnamese culture through their fashion products, TiredCity and BARO not only appeal to the local market but also attract international customers. This integration of cultural elements helps foster cross-cultural understanding and appreciation, contributing to cultural diversity and the development of the Vietnamese fashion industry

Asian Values and Human Rights: A Vietnamese Perspective

This paper examines the impact of the ideology of ‘Asian Values' on the legal norms and practices that frame the recognition and protection of human rights in Vietnam. Specifically, the paper focusses on the extent to which Asian Values has been deployed to discourage the adoption of international human rights norms and practices in the context of Vietnam’s rapid economic development since the mid- 1980s. The paper first sketches the adoption of Asian Values in Vietnam’s politics and society. Cultural and political factors that have shaped the conception of human rights are reviewed. Human rights language and norms, as manifest in political ideologies, policies and laws are then analysed, with particular reference to the different versions of Vietnam’s Constitution. It is shown that both the Communist Party of Vietnam (CPV) and the State of Vietnam have clearly articulated Asian Values in formulating their conceptions of human rights. This outcome is argued to result from the fact that Vietnamese political leaders, alike with Lee Kwan Yew in Singapore, the progenitor of Asian Rights, have been strongly influenced by Confucian ideals of governance. Confucianism is not, however, the only basis for political ideas in Vietnam. Although Vietnam is a market economy it remains a one- party state  controlled  by  the  CPV.  The  Marxist-Leninist  principles  on  which the current State of Vietnam was based at its inception in 1975 remain intact. This ideology was however layered onto generations of collectivist principles embodied in the dominant agrarian society. The influence of Asian Values, on the recognition of and support for human rights in Vietnam has, however, been largely negative rather than positive, especially in relation to recognising civil and political rights as codified in universal human rights instruments. Thus, the protection and promotion of human rights in Vietnam, going forward, essentially mandates eliminating the influence of Asian Values in the ideology of political leaders and in the wider society. Key words: Human rights, Asian Values, democracy, constitution, Communist Party, Vietna

The impact of employer branding on job application intention: Evidence from business undergraduates in Vietnam

This study aims to figure out the impact of employer branding perception on job application intention of business undergraduates in three main provinces of Southeast Vietnam, including Binh Duong, Dong Nai, and Ho Chi Minh City. The result shows that Task Attractiveness, Payment Attractiveness, and Working Atmosphere positively affect business undergraduates’ job application intention. However, our findings also show that the participants do not put a lot of attention on the Work-life Comfort factor and the Career Opportunities factor