Notation: Given , we set and . We also set . The model We consider a league of teams denoted by whose initial random strengths are denoted by . In the league every team plays matches, one against each of the remaining teams . Note that there are in total matches in the league. These …
We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family of permutations avoiding a fixed set of patterns, we study the limit of proportions of consecutive patterns on large permutations of . These limits form a region, which we call the pattern-avoiding feasible region for . We show that, …
Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant, called tandem walks, are well-known to be related to each other through several bijections. We introduce a further new family of discrete objects, called coalescent-walk processes and we relate it to the three families mentioned above. We prove joint Benjamini–Schramm …