As the Rugby Championship heads into round two, the Springboks will be seeking redemption against the Wallabies, while the All Blacks will aim to secure successive wins against Argentina – and ...

The Cricketer looks at what each of the counties in contention to reach the next stage needs to keep alive their hopes of going all the way ...

Paris Saint-Germain have booked their place in the Club World Cup knockout stage after a comfortable 2-0 win against Seattle Sounders at Lumen Field. Khvicha Kvaratskhelia and Achraf Hakimi got the ...

The Athletic has live coverage of Juventus vs Manchester City from the 2025 FIFA Club World Cup. The group stage at the FIFA Club World Cup has now been completed, with the top two teams in each of ...

THE All-Ireland SFC group stages are set for a dramatic conclusion this weekend with six of Ulster’s seven participants still unsure of what their path to Sam will look like. For All-Ireland champions ...

Chelsea will learn their Champions League qualification fate against Nottingham Forest on Sunday afternoon at the City Ground. Enzo Maresca's side have one final game to play in the Premier League and ...

Wednesday brings the end of the Champions League league phase with Matchday 8, which could bring chaos unparalleled in the history of the tournament, maybe even the sport. All 36 teams will be in ...

The UEFA Champions League returns on Wednesday with Matchday 8 and it has the potential to be a historically chaotic day in terms of results that the sport has ever seen. All 36 teams will be in ...

Liverpool fans won’t need to be reminded that we sit top of the Champions League group stage as the only team to have a 100% record in the competition. With two games remaining, the permutations for ...

In combinatorics, permutations are important objects with many operations. In this paper, we define a coupling product on permutations and prove that the space spanned by permutations is a graded ...