Two vignettes on full rook placements

نویسندگان

  • Jonathan Bloom
  • Vincent Vatter
چکیده

Using bijections between pattern-avoiding permutations and certain full rook placements on Ferrers boards, we give short proofs of two enumerative results. The first is a simplified enumeration of the 3124, 1234avoiding permutations, obtained recently by Callan via a complicated decomposition. The second is a streamlined bijection between 1342-avoiding permutations and permutations which can be sorted by two increasing stacks in series, originally due to Atkinson, Murphy, and Ruškuc.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Bijections on m-level rook placements

Suppose the rows of a board are partitioned into sets of m rows called levels. An m-level rook placement is a subset of the board where no two squares are in the same column or the same level. We construct explicit bijections to prove three theorems about such placements. We start with two bijections between Ferrers boards having the same number of m-level rook placements. The first generalizes...

متن کامل

q-Rook placements and Jordan forms of upper-triangular nilpotent matrices

The set of n by n upper-triangular nilpotent matrices with entries in a finite field Fq has Jordan canonical forms indexed by partitions λ ` n. We study a connection between these matrices and non-attacking q-rook placements, which leads to a combinatorial formula for the number Fλ(q) of matrices of fixed Jordan type as a weighted sum over rook placements. Résumé. L’ensemble des matrices triang...

متن کامل

Pattern Avoidance in the Rook Monoid

We consider two types of pattern avoidance in the rook monoid, i.e. the set of 0–1 square matrices with at most one nonzero entry in each row and each column. For one-dimensional rook patterns, we completely characterize monoid elements avoiding a single pattern of length at most three and develop an enumeration scheme algorithm to study rook placements avoiding sets of patterns.

متن کامل

Rook Placements in Young Diagrams and Permutation Enumeration

Abstract. Given two operators M and N subject to the relation MN −qNM = p, and a word w in M and N , the rewriting of w in normal form is combinatorially described by rook placements in a Young diagram. We give enumerative results about these rook placements, particularly in the case where p = (1−q)/q. This case naturally arises in the context of the PASEP, a random process whose partition func...

متن کامل

2 7 N ov 2 00 8 Matrix Ansatz , lattice paths and rook placements

We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP. Besides other interpretations, this formula gives the generating function for permutations of a given size with respect to the number of ascents and occurrence...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Australasian J. Combinatorics

دوره 64  شماره 

صفحات  -

تاریخ انتشار 2016