2 citations · 3 across the 5 of their papers we have counts for
7 papers
A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem
Nicholas A. Loehr, Bruce E. Sagan, Gregory S. Warrington
Consider lattice paths in Z^2 taking unit steps north (N) and east (E). Fix positive integers r,s and put an equivalence relation on points of Z^2 by letting v,w be equivalent if v…
The combinatorics of a three-line circulant determinant
Nicholas A. Loehr, Gregory S. Warrington, Herbert S. Wilf
We study the determinant of the pxp circulant matrix whose first row is (1,-x,0,...,0,-y,0,...,0), the -y being in position q+1. The coefficients of this polynomial are integers th…
Juggling probabilities
Gregory S. Warrington
The act of a person juggling can be viewed as a Markov process if we assume that the juggler throws to random heights. I make this association for the simplest reasonable model of…
Counterexamples to the 0-1 conjecture
Timothy J. McLarnan, Gregory S. Warrington
For permutations x and w, let mu(x,w) be the coefficient of highest possible degree in the Kazhdan-Lusztig polynomial P_{x,w}. It is well-known that the coefficients mu(x,w) arise…
Two formulae for inverse Kazhdan-Lusztig polynomials in S_n
Gregory S. Warrington
Let w_0 denote the permutation [n,n-1,...,2,1]. We give two new explicit formulae for the Kazhdan-Lusztig polynomials P_{w_0w,w_0x} in S_n when x is a maximal element in the singul…
Maximal singular loci of Schubert varieties in SL(n)/B
Sara C. Billey, Gregory S. Warrington
We give an explicit combinatorial description of the irreducible components of the singular locus of the Schubert variety X_w for any element w in S_n. Our description of the irred…