Add to ORKGIn this paper a kind of generalized Pascal triangle is coustructed whose k'th entry in its n'th row equals the number of permutations of degree n having exactly k inversions. Let p~ be the number of the n-degree permutations having: exactly le inversions. Then pk J1 (n) , 1 > ') T • O. if k
AbstractIn response to some recent questions of L.W. Shapiro, we develop a theory of triangular arra...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliogr...
Based on two inversion formulas for enumerating words in the free monoid by adjacencies, we present ...
AbstractWhen a list of size n is nearly sorted, a straight insertion sort algorithm is highly effici...
Permutations consisting of a single cycle are considered. EDELMAN (1987) proved that such permutatio...
When a list of size n is nearly sorted, a straight insertion sort algorithm is highly efficient sinc...
AbstractWe define a new combinatorial statistic, maximal-inversion, on a permutation. We remark that...
This work provides a criterion for a binary strictly upper triangle matrices to be a matrix of inver...
We present a short proof of MacMahon's classic result that the number of permutations with $k$ inver...
The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nea...
In this paper we will recall the inversion algorithm described in [1]. The algorithm classifies poly...
AbstractWe use basic properties of infinite lower triangular matrices and the connections of Toeplit...
We consider two families of Pascal-like triangles that have all ones on the left side and ones separ...
Permutations that avoid given patterns have been studied in great depth for their connections to oth...
Every polynomial of degree n has n roots; every continuous function on [0, 1] attains its maximum; e...
AbstractIn response to some recent questions of L.W. Shapiro, we develop a theory of triangular arra...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliogr...
Based on two inversion formulas for enumerating words in the free monoid by adjacencies, we present ...
AbstractWhen a list of size n is nearly sorted, a straight insertion sort algorithm is highly effici...
Permutations consisting of a single cycle are considered. EDELMAN (1987) proved that such permutatio...
When a list of size n is nearly sorted, a straight insertion sort algorithm is highly efficient sinc...
AbstractWe define a new combinatorial statistic, maximal-inversion, on a permutation. We remark that...
This work provides a criterion for a binary strictly upper triangle matrices to be a matrix of inver...
We present a short proof of MacMahon's classic result that the number of permutations with $k$ inver...
The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nea...
In this paper we will recall the inversion algorithm described in [1]. The algorithm classifies poly...
AbstractWe use basic properties of infinite lower triangular matrices and the connections of Toeplit...
We consider two families of Pascal-like triangles that have all ones on the left side and ones separ...
Permutations that avoid given patterns have been studied in great depth for their connections to oth...
Every polynomial of degree n has n roots; every continuous function on [0, 1] attains its maximum; e...
AbstractIn response to some recent questions of L.W. Shapiro, we develop a theory of triangular arra...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliogr...
Based on two inversion formulas for enumerating words in the free monoid by adjacencies, we present ...