This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165208 #11 Oct 07 2024 06:32:29 %S A165208 1,1,5,210,162482,3431771334,2675532842827606,98099380263646542332472, %T A165208 207159998877655913898903666460600, %U A165208 29992398464230524512087152790819658487446680 %N A165208 The number of maximal paths in the Bruhat graph for S_n. %C A165208 The Bruhat graph on S_n is the directed graph with an edge connecting v to w whenever v and w differ by a transposition and w has more inversions than v. A maximal path in the Bruhat graph on S_n is one which goes from the identity element to the longest permutation [n,n-1,..., 2,1] written in one-line notation. Note, the Bruhat graph has more edges than the Hasse diagram for the Bruhat order. For example in S_3, [123] is connected to [321] in the Bruhat graph because they differ by a single transposition. %D A165208 Anders Bjorner and Francesco Brenti, "Combinatorics of Coxeter Groups". Graduate Texts in Mathematics, 231. Springer, New York, 2005. %D A165208 James Carrell, "The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties". Proceedings of Symposia in Pure Math., 56 (1994), 53--61. %H A165208 Francesco Brenti, <a href="https://doi.org/10.1090/S0894-0347-98-00249-5">Lattice paths and Kazhdan-Lusztig polynomials</a>, J. Amer. Math. Soc., 11 (1998), 229-259. %Y A165208 Cf. A061710. %K A165208 hard,nonn %O A165208 1,3 %A A165208 _Sara Billey_, Sep 07 2009