title: Near-automorphisms of Latin squares

authors: Cavenagh, Nicholas J.

subjects: intercalate

abstract: We define a near-automorphism α of a Latin square L to be an isomorphism such that L and αL differ only within a 2 × 2 subsquare. We prove that for all n≥2 except n∈{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if α has the cycle structure (2, n − 2), then L exists if and only if n≡2 (mod 4), and can be constructed from a special type of partial orthomorphism. Along the way, we generalize a theorem by Marshall Hall, which states that any Latin rectangle can be extended to a Latin square. We also show that if α has at least 2 fixed points, then L must contain two disjoint non-trivial subsquares.

text: Near-automorphisms of Latin squares We define a near-automorphism α of a Latin square L to be an isomorphism such that L and αL differ only within a 2 × 2 subsquare. We prove that for all n≥2 except n∈{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if α has the cycle structure (2, n − 2), then L exists if and only if n≡2 (mod 4), and can be constructed from a special type of partial orthomorphism. Along the way, we generalize a theorem by Marshall Hall, which states that any Latin rectangle can be extended to a Latin square. We also show that if α has at least 2 fixed points, then L must contain two disjoint non-trivial subsquares.

year: 2011

title: Dark clouds on the horizon

authors: Barbour, Karen

abstract: In the face of our current political and economic environment, particularly in the context of education, community and arts, dark clouds on our horizon have fast become storms. Storms raining down on us in the South Pacific with a force and subsequent devastation that is soul destroying. Some days I feel we might be in the eye of the storm and other days a glimmer of light sparkles off the rain from the aspirational agendas of UNESCO and our international organisations. But most days, it is dark clouds and storms. Thundering requests for more evidence, gales of economic cuts poorly disguised as enhancement projects, and rain that no arts educator can withstand alone. Where is the sheltering umbrella for a dancing academic in the university? This presentation is a critical autoethnography of hope embodied, a practice of withdrawing to the shelter in my own skin to survive this storm.

text: Dark clouds on the horizon In the face of our current political and economic environment, particularly in the context of education, community and arts, dark clouds on our horizon have fast become storms. Storms raining down on us in the South Pacific with a force and subsequent devastation that is soul destroying. Some days I feel we might be in the eye of the storm and other days a glimmer of light sparkles off the rain from the aspirational agendas of UNESCO and our international organisations. But most days, it is dark clouds and storms. Thundering requests for more evidence, gales of economic cuts poorly disguised as enhancement projects, and rain that no arts educator can withstand alone. Where is the sheltering umbrella for a dancing academic in the university? This presentation is a critical autoethnography of hope embodied, a practice of withdrawing to the shelter in my own skin to survive this storm.

year: 2016

title: Speaking the unspoken: Maori experiences of racism in New Zealand sport

authors: Hippolite, Holly Raima

subjects: Maori

abstract: This research explores how being Maori influences Maori participants’ sport experiences and offers a critical Maori perspective on New Zealand sport. Ten experienced Maori sport participants were interviewed using Kaupapa Maori Research Methods which involved research performed by Maori, about Maori being Maori. This research grew out of discussions with Maori participants and explores their experiences as athletes, coaches, administrators and spectators, focusing on their interactions with Pakeha in Pakeha-dominated sport. Their experiences demonstrate personal, cultural and institutional racism in New Zealand sport and indicate how the power differentials in society impact on the ability of Maori to practice important cultural values in Pakeha-dominated contexts. I argue that racism is a factor affecting the relationships of Maori with Pakeha in key functionary positions in sport and identify a culture of denial that operates to marginalise discussions about racism generally. These participants’ experiences reflect cultural incapacity and blindness (Cross, Bazron, Dennis & Isaacs, 1989) by the dominant culture which have negative effects on the Maori participants including decisions to opt out of sport, feelings of hurt and frustration, a reduction in their commitment to national identity and a general sense that they are not considered as equals. The conclusion considers what is needed for New Zealand sport to become fully culturally inclusive; a situation desired by the participants and which has the potential to benefit everyone in sport.

text: Speaking the unspoken: Maori experiences of racism in New Zealand sport This research explores how being Maori influences Maori participants’ sport experiences and offers a critical Maori perspective on New Zealand sport. Ten experienced Maori sport participants were interviewed using Kaupapa Maori Research Methods which involved research performed by Maori, about Maori being Maori. This research grew out of discussions with Maori participants and explores their experiences as athletes, coaches, administrators and spectators, focusing on their interactions with Pakeha in Pakeha-dominated sport. Their experiences demonstrate personal, cultural and institutional racism in New Zealand sport and indicate how the power differentials in society impact on the ability of Maori to practice important cultural values in Pakeha-dominated contexts. I argue that racism is a factor affecting the relationships of Maori with Pakeha in key functionary positions in sport and identify a culture of denial that operates to marginalise discussions about racism generally. These participants’ experiences reflect cultural incapacity and blindness (Cross, Bazron, Dennis & Isaacs, 1989) by the dominant culture which have negative effects on the Maori participants including decisions to opt out of sport, feelings of hurt and frustration, a reduction in their commitment to national identity and a general sense that they are not considered as equals. The conclusion considers what is needed for New Zealand sport to become fully culturally inclusive; a situation desired by the participants and which has the potential to benefit everyone in sport.

year: 2010