Let λ be a partition, and denote by fλ the number of standard tableaux of shape λ. The asymptotic shape of λ maximizing fλ was determined in the classical work of Logan and S...
Let G = (V, E) be any d-regular graph with girth g on n vertices, for d ≥ 3. This note shows that G has a maximum matching which includes all but an exponentially small fraction...
We determine the limiting distributions of the longest alternating subsequence for pattern-restricted permutations in which the pattern is any one of the six patterns of length th...
We introduce and develop a two-parameter chromatic symmetric function for a simple graph G over the field of rational functions in q and t , Q (q, t). We derive its expansion in ...
A closed knight’s tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated i...