Buchacher, Manfred Hofmanninger, Sophie Kauers, Manuel
Published in
Annals of Combinatorics

We provide some first experimental data about generating functions of restricted lattice walks with small steps in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ma...

Morrill, Thomas
Published in
Annals of Combinatorics

We generalize the generating series of the Dyson ranks and M2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_2$$\end{document}-ranks of overpartitions to obtain k-fol...

d’Azevedo, Antonio Breda Catalano, Domenico A. Širáň, Jozef
Published in
Annals of Combinatorics

Bi-orientable maps (also called pseudo-orientable maps) were introduced by Wilson in the 1970s to describe non-orientable maps with the property that opposite orientations can consistently be assigned to adjacent vertices. In contrast to orientability, which is both a combinatorial and topological property, bi-orientability is only a combinatorial ...

Ehrenborg, Richard Happ, Alex
Published in
Annals of Combinatorics

We give a short proof that the f-vector of the descent polytope DPv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{DP}\,}}_{\mathbf {v}}$$\end{document} is ...

Pearce, Geoffrey Praeger, Cheryl E.
Published in
Annals of Combinatorics

A graph is Cartesian decomposable if it is isomorphic to a Cartesian product of strictly smaller graphs, each of which has more than one vertex and admits no such decomposition. These smaller graphs are called the Cartesian-prime factors of the Cartesian decomposition, and were shown, by Sabidussi and Vizing independently, to be uniquely determined...

Yang, Mingjia
Published in
Annals of Combinatorics

Enumeration problems related to words avoiding patterns as well as permutations that contain the pattern 123 exactly once have been studied in great detail. However, the problem of enumerating words that contain the pattern 123 exactly once is new and will be the focus of this paper. Previously, Zeilberger provided a shortened version of Burstein’s...

Mustapha, Sami
Published in
Annals of Combinatorics

We prove that the sequence enΓn∈N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( e_n^{\Gamma }\right) _{n\in \mathbb {N}}$$\end{document} of numbers of excursion...

Kusunoki, Takuya Murai, Satoshi
Published in
Annals of Combinatorics

A basic combinatorial invariant of a convex polytope P is its f-vector f(P)=(f0,f1,⋯,fdimP-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(P)=(f_0,f_1,\dots ,f_{\di...

Kantarcı Oğuz, Ezgi
Published in
Annals of Combinatorics

In 2015, Jing and Li defined type B quasisymmetric Schur functions and conjectured that these functions have a positive, integral and unitriangular expansion into peak functions. We prove this conjecture, and refine their combinatorial model to give explicit expansions in monomial, fundamental and peak bases. We also show that these functions are n...

Roche-Newton, Oliver Shparlinski, Igor E. Winterhof, Arne
Published in
Annals of Combinatorics

Balog and Wooley have recently proved that any subset A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} of either real numbers or of a pri...