title: Defining sets and critical sets in (0,1)-matrices.

authors: Cavenagh, Nicholas J.

subjects: (0,1)-matrix

abstract: If D is a partially filled-in (0, 1)-matrix with a unique completion to a (0, 1)-matrix M (with prescribed row and column sums), we say that D is a defining set for M. If the removal of any entry of D destroys this property (i.e. at least two completions become possible), we say that D is a critical set for M. In this note, we show that the complement of a critical set for a (0, 1)-matrix M is a defining set for M. We also study the possible sizes (number of filled-in cells) of defining sets for square matrices M with uniform row and column sums, which are also frequency squares. In particular, we show that when the matrix is of even order 2m and the row and column sums are all equal to m, the smallest possible size of a critical set is precisely m². We give the exact structure of critical sets with this property.

text: Defining sets and critical sets in (0,1)-matrices. If D is a partially filled-in (0, 1)-matrix with a unique completion to a (0, 1)-matrix M (with prescribed row and column sums), we say that D is a defining set for M. If the removal of any entry of D destroys this property (i.e. at least two completions become possible), we say that D is a critical set for M. In this note, we show that the complement of a critical set for a (0, 1)-matrix M is a defining set for M. We also study the possible sizes (number of filled-in cells) of defining sets for square matrices M with uniform row and column sums, which are also frequency squares. In particular, we show that when the matrix is of even order 2m and the row and column sums are all equal to m, the smallest possible size of a critical set is precisely m². We give the exact structure of critical sets with this property.

year: 2013

title: Canberra-planning cross-linguistic disagreement: a few remarks

authors: Wyatt, Jeremy

abstract: My remarks will focus on two questions:
• What methods should we use in investigating the nature of disagreement?
• What do these methods tell us about the possibility of cross-linguistic disagreement?

text: Canberra-planning cross-linguistic disagreement: a few remarks My remarks will focus on two questions:
• What methods should we use in investigating the nature of disagreement?
• What do these methods tell us about the possibility of cross-linguistic disagreement?

year: 2022

title: KAUMĀTUATANGA  Supporting School Leaders To Develop Cultural Values While Resisting The Dominance of Colonialism

authors: Nuri, Ngahuia

subjects: Kaumātua

abstract: In an education system that is asserting to the importance of Māori (indigenous people of Aotearoa) language, culture, identity and the history of Aotearoa  (New Zealand) into the curriculum, there is direction from the Ministry of Education (MOE) for schools to reach out to iwi. What this looks like and how this can be achieved is not an easy task. This thesis follows the journey of three kaumātua (respected, knowledgeable elders, both female and male) working alongside the Senior Leadership Team (SLT) of a decile 10 kura auraki (mainstream primary school) where ākonga Māori (Māori students) were in the minority. The research examines what role kaumātua might have in guiding other schools to help tamariki Māori (Māori children) enjoy and achieve education success as Māori. It highlights the coming together of leaders from two different worldviews with this vision as a common purpose. 

Kaumātua in te ao Māori (the Māori world) are respected elders. Kaumātua are leaders, respected for their wisdom, knowledge and models of behaviour among other attributes. The Māui narratives are one example of demonstrating the characteristics of kaumātua. It was through his respected elders that Maui achieved so much. It was his grandfather who rescued him and taught him all he knew. It was his grandmother Mahuika who gave him fire and it was his kuia (female elder) Murirangiwhenua from whom he received the magic jawbone. The wisdom of Māori kaumātua has been recognised for centuries by Māori and yet kaumātua are often an untapped resource in the mainstream sector of education. In this thesis the kaumātua and members of the SLT share their experiences of working together and the learning and unlearning that has taken place over a period of four years from 2016 through 2019. They share their vulnerability, humility and strength in the goals they have worked towards over this period of time.

text: KAUMĀTUATANGA  Supporting School Leaders To Develop Cultural Values While Resisting The Dominance of Colonialism In an education system that is asserting to the importance of Māori (indigenous people of Aotearoa) language, culture, identity and the history of Aotearoa  (New Zealand) into the curriculum, there is direction from the Ministry of Education (MOE) for schools to reach out to iwi. What this looks like and how this can be achieved is not an easy task. This thesis follows the journey of three kaumātua (respected, knowledgeable elders, both female and male) working alongside the Senior Leadership Team (SLT) of a decile 10 kura auraki (mainstream primary school) where ākonga Māori (Māori students) were in the minority. The research examines what role kaumātua might have in guiding other schools to help tamariki Māori (Māori children) enjoy and achieve education success as Māori. It highlights the coming together of leaders from two different worldviews with this vision as a common purpose. 

Kaumātua in te ao Māori (the Māori world) are respected elders. Kaumātua are leaders, respected for their wisdom, knowledge and models of behaviour among other attributes. The Māui narratives are one example of demonstrating the characteristics of kaumātua. It was through his respected elders that Maui achieved so much. It was his grandfather who rescued him and taught him all he knew. It was his grandmother Mahuika who gave him fire and it was his kuia (female elder) Murirangiwhenua from whom he received the magic jawbone. The wisdom of Māori kaumātua has been recognised for centuries by Māori and yet kaumātua are often an untapped resource in the mainstream sector of education. In this thesis the kaumātua and members of the SLT share their experiences of working together and the learning and unlearning that has taken place over a period of four years from 2016 through 2019. They share their vulnerability, humility and strength in the goals they have worked towards over this period of time.

year: 2024