The authors consider the length, $ l_N $, of the longest increasing subsequence of a
random permutation of $ N $ numbers. The main result in this paper is a proof that the …

Permutation groups are one of the oldest topics in algebra. Their study has recently been
revolutionized by new developments, particularly the Classification of Finite Simple Groups …

Abstract In a 1972 paper, Germain Kreweras investigated noncrossing partitions under the
refinement order relation. His paper set the stage both for a wealth of further enumerative …

We survey a number of models from physics, statistical mechanics, probability theory and
combinatorics, which are each described in terms of an orthogonal polynomial ensemble …

We show that the moments of the trace of a random unitary matrix have combinatorial
interpretations in terms of longest increasing subsequences of permutations. To be precise …

The colored HOMFLY polynomial is the quantum invariant of oriented links in $ S^ 3$
associated with irreducible representations of the quantum group $ U_q (\mathrm {sl} _N) …

Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on
the subject of symmetric groups and representation theory. Utilizing new research and …

We study the fluctuations, in the large deviations regime, of the longest increasing sub-
sequence of a random iid sample on the unit square. In particular, our results yield the …

Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of
enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective …

We define and characterizeswitching, an operation that takes two tableaux sharing a
common border and “moves them through each other” giving another such pair. Several …