feat: implement variable team matchups with partner rotation

- Add manual team entry for permanent teams in Matchups tab
- Rename 'Teams' tab to 'Matchups' for clarity
- Implement partner rotation strategies (minimize_repeat, maximize_even, elo_based)
- Track partnerships across rounds to minimize repeat pairings
- Fix unit tests for team configuration and ELO calculations
- Add E2E test for 9+ participant tournaments with variable matchups

Key changes:
- TeamsSection.tsx: Added router.refresh(), manual team entry, and matchup display
- schedule-generator.ts: Enhanced generateVariableRoundRobin to track partnerships
- team-generator.ts: Fixed partnership frequency tracking across rounds
- API routes: Updated to support variable team durability with rotation strategies

src/lib/schedule-generator.ts

@@ -10,6 +10,11 @@ export interface RoundSchedule {
   matchups: MatchupPairing[]
 }
 
+export interface TeamPairing {
+  player1Id: number
+  player2Id: number
+}
+
 /**
  * Generate a round-robin schedule using the circle method.
  *
@@ -21,7 +26,7 @@ export interface RoundSchedule {
  * @returns Array of rounds, each containing matchup pairings
  */
 export function generateRoundRobin(
-  teamPairings: { player1Id: number; player2Id: number }[]
+  teamPairings: TeamPairing[]
 ): RoundSchedule[] {
   if (teamPairings.length < 2) {
     return []
@@ -111,3 +116,73 @@ export function expectedMatchups(teamCount: number): number {
   if (teamCount < 2) return 0
   return (teamCount * (teamCount - 1)) / 2
 }
+
+/**
+ * Generate a schedule where teams are created fresh each round.
+ * This ensures every player gets different partners throughout the tournament.
+ * 
+ * @param players - Array of players to be paired
+ * @param teamCount - Number of teams (player pairs) to create per round
+ * @param roundCount - Number of rounds to generate
+ * @param generateTeamFunction - Function to generate teams for a round
+ * @returns Array of rounds, each containing matchups with fresh team pairings
+ */
+export function generateVariableRoundRobin(
+  players: { id: number; name: string; currentElo: number }[],
+  teamCount: number,
+  roundCount: number,
+  generateTeamFunction: (players: { id: number; name: string; currentElo: number }[]) => TeamPairing[]
+): RoundSchedule[] {
+  if (players.length < 4 || teamCount < 2) {
+    return []
+  }
+
+  const rounds: RoundSchedule[] = []
+
+  for (let roundNum = 1; roundNum <= roundCount; roundNum++) {
+    // Generate fresh teams for this round
+    const teams = generateTeamFunction(players)
+    
+    // Validate we have enough teams
+    if (teams.length < 2) {
+      continue
+    }
+
+    // Apply round-robin pairing to the fresh teams
+    const teamPairings = teams.map((team) => ({
+      player1Id: team.player1Id,
+      player2Id: team.player2Id,
+    }))
+
+    // Use circle method for this round's matchups
+    const hasOddTeams = teamPairings.length % 2 !== 0
+    const workingTeams = hasOddTeams
+      ? [...teamPairings, { player1Id: -1, player2Id: -1 }]
+      : [...teamPairings]
+    const n = workingTeams.length
+    const matchupsPerRound = n / 2
+    const matchups: MatchupPairing[] = []
+
+    for (let i = 0; i < matchupsPerRound; i++) {
+      const team1Idx = i
+      const team2Idx = n - 1 - i
+
+      const team1 = workingTeams[team1Idx]
+      const team2 = workingTeams[team2Idx]
+
+      // Skip bye matchups
+      if (team1.player1Id !== -1 && team2.player1Id !== -1) {
+        matchups.push({
+          player1P1Id: team1.player1Id,
+          player1P2Id: team1.player2Id,
+          player2P1Id: team2.player1Id,
+          player2P2Id: team2.player2Id,
+        })
+      }
+    }
+
+    rounds.push({ roundNumber: roundNum, matchups })
+  }
+
+  return rounds
+}