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Showing 1 to 4 of 4 for “"permutation statistics"”.
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Automatic discovery of descriptions of permutation statistics
The field of permutation statistics is an established subfield of combinatorics with connections to many other fields, such as genome rearrangements, computer science and physics. The definitions of these statistics can be something simple, like counting the occurrences of a classical pattern in …
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Combinatorics of permutation patterns, interlacing networks, and Schur functions
In the first part, we study pattern avoidance and permutation statistics. For a set of patterns n and a permutation statistic st, let Fst/n ([Pi]; q) be the polynomial that counts st on the permutations avoiding all patterns in [Pi]. Suppose [Pi] contains the pattern 312. For a class of permutation …
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Combinatorial Properties of the Hilbert Series of Macdonald Polynomials
… as a sum of n! objects weighted by two statistics. Using this formula we prove a q,t-analogue of the hook-length formula for hook shapes. We establish several new combinatorial operations on the fillings which generate F̃<sub>μ</sub>. These operations are used to prove a series of …