849 research outputs found
Quadrant marked mesh patterns in 123-avoiding permutations
Given a permutation in the symmetric
group , we say that matches the quadrant marked
mesh pattern in if there are at least
points to the right of in which are greater than
, at least points to the left of in which are
greater than , at least points to the left of in
which are smaller than , and at least points to the
right of in which are smaller than . Kitaev,
Remmel, and Tiefenbruck systematically studied the distribution of the number
of matches of in 132-avoiding permutations. The
operation of reverse and complement on permutations allow one to translate
their results to find the distribution of the number of
matches in 231-avoiding, 213-avoiding, and 312-avoiding permutations. In this
paper, we study the distribution of the number of matches of
in 123-avoiding permutations. We provide explicit
recurrence relations to enumerate our objects which can be used to give closed
forms for the generating functions associated with such distributions. In many
cases, we provide combinatorial explanations of the coefficients that appear in
our generating functions
Lil Ommi
Ä abra ta’ poeżiji u proża li tinkludi: Għal Professjoni ta’ Soru ta’ Dun Pawl – Kelb Rieqed La Tqajmux ta’ T. Z. – Lil Ommi ta’ C. M. B.N/
Nofs ta' kelma
Ä abra ta’ poeżiji u proża li tinkludi: Alla kbir bla qies! ta’ R. M. B. – Tantum ergo – Lil kewkba feÄ¡Ä¡a – Għajjiena le xebagħna ta’ Ros. Briffa – Sliem ta’ Dun Karm – Kewkba ta’ Dun Karm – Nofs ta’ kelma ta’ A. C.N/
Alla! Alla!
Ä abra ta’ poeżiji u proża li tinkludi: Il-Għanja tal-Għid ta’ Sajdun – Nofs-inhar Sajfi ta’ Rosario Briffa – Min kien Jusef ta’ G. B. – L-Hinn min-Natura Hemm Alla! ta’ Dun Karm – Il-Flus tal-Ħares ta’ T. Z. – Alla! Alla! ta’ C. M. B.N/
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