Zobrazeno 1 - 10
of 44
pro vyhledávání: '"McNamara, Peter R. W."'
A famous conjecture of Stanley states that his chromatic symmetric function distinguishes trees. As a quasisymmetric analogue, we conjecture that the chromatic quasisymmetric function of Shareshian and Wachs and of Ellzey distinguishes directed trees
Externí odkaz:
http://arxiv.org/abs/2201.11763
We seek simple conditions on a pair of labeled posets that determine when the difference of their $(P,\omega)$-partition enumerators is $F$-positive, i.e., positive in Gessel's fundamental basis. This is a quasisymmetric analogue of the extensively s
Externí odkaz:
http://arxiv.org/abs/2006.10087
Autor:
Dukes, Mark, McNamara, Peter R. W.
The combined work of Bousquet-M\'elou, Claesson, Dukes, Jel\'inek, Kitaev, Kubitzke and Parviainen has resulted in non-trivial bijections among ascent sequences, (2+2)-free posets, upper-triangular integer matrices, and pattern-avoiding permutations.
Externí odkaz:
http://arxiv.org/abs/1807.11505
Publikováno v:
Ann. Comb. 24 (2020), no. 1, 69-93
We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce
Externí odkaz:
http://arxiv.org/abs/1708.00513
Publikováno v:
Lattice Path Combinatorics and Applications, G. E. Andrews, C. Krattenthaler, A. Krinik (Eds.), Springer, 2019, 155-165
We consider a class of lattice paths with certain restrictions on their ascents and down steps and use them as building blocks to construct various families of Dyck paths. We let every building block $P_j$ take on $c_j$ colors and count all of the re
Externí odkaz:
http://arxiv.org/abs/1602.03550
Publikováno v:
S\'eminaire Lotharingien de combinatoire, vol.80, article B80d (2019)
We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As applications we give
Externí odkaz:
http://arxiv.org/abs/1509.02581
Autor:
Elizalde, Sergi, McNamara, Peter R. W.
Publikováno v:
International Mathematics Research Notices, 2018 (7), 2099-2034
The consecutive pattern poset is the infinite partially ordered set of all permutations where $\sigma\le\tau$ if $\tau$ has a subsequence of adjacent entries in the same relative order as the entries of $\sigma$. We study the structure of the interva
Externí odkaz:
http://arxiv.org/abs/1508.05963
Autor:
Billey, Sara C., McNamara, Peter R. W.
Publikováno v:
The Mathematical Legacy of Richard P. Stanley, P. Hersh, T. Lam, P. Pylyavskyy, and V. Reiner (Eds.), American Mathematical Society, 2016, 83-104
We weave together a tale of two rings, SYM and QSYM, following one gold thread spun by Richard Stanley. The lesson we learn from this tale is that "Combinatorial objects like to be counted by quasisymmetric functions."
Comment: 22 pages, 3 figur
Comment: 22 pages, 3 figur
Externí odkaz:
http://arxiv.org/abs/1505.01115
Autor:
McNamara, Peter R. W.
Publikováno v:
J. Combin., 5 (1) (2014) 51-85
Reiner, Shaw and van Willigenburg showed that if two skew Schur functions s_A and s_B are equal, then the skew shapes A and B must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weake
Externí odkaz:
http://arxiv.org/abs/1307.6233
Publikováno v:
Journal of Combinatorial Theory, Series A, 134 (2015), pp. 1-35
The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected su
Externí odkaz:
http://arxiv.org/abs/1305.5569