Camillia Smith Barnes - Enumeration of the distinct shuffles of permutations

dmtcs:2718 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2718
Enumeration of the distinct shuffles of permutationsArticle

Authors: Camillia Smith Barnes 1

  • 1 Department of Mathematics [Cambridge]

A shuffle of two words is a word obtained by concatenating the two original words in either order and then sliding any letters from the second word back past letters of the first word, in such a way that the letters of each original word remain spelled out in their original relative order. Examples of shuffles of the words $1234$ and $5678$ are, for instance, $15236784$ and $51236748$. In this paper, we enumerate the distinct shuffles of two permutations of any two lengths, where the permutations are written as words in the letters $1,2,3,\ldots ,m$ and $1,2,3,\ldots ,n$, respectively.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: shuffles,permutations,enumeration,Catalan numbers,Shuffle Algebra,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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