Related papers: Fully packed loop configurations: polynomiality an…
We show that the number of fully packed loop configurations corresponding to a matching with $m$ nested arches is polynomial in $m$ if $m$ is large enough, thus essentially proving two conjectures by Zuber [Electronic J. Combin. 11 (2004),…
Two conjectures of Zuber [``On the counting of fully packed loops configurations. Some new conjectures,'' preprint] on the enumeration of configurations in the fully packed loop model on the square grid with periodic boundary conditions,…
The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular…
Fully Packed Loop configurations (FPLs) are certain configurations on the square grid, naturally refined according to certain link patterns. If $A_X$ is the number of FPLs with link pattern $X$, the Razumov--Stroganov correspondence…
Fully Packed Loop configurations in a triangle (TFPLs) first appeared in the study of ordinary Fully Packed Loop configurations (FPLs) on the square grid where they were used to show that the number of FPLs with a given link pattern that…
We are interested in the enumeration of Fully Packed Loop configurations on a grid with a given noncrossing matching. By the recently proved Razumov--Stroganov conjecture, these quantities also appear as groundstate components in the…
Triangular fully packed loop configurations (TFPLs) came up in the study of fully packed loop configurations on a square (FPLs) corresponding to link patterns with a large number of nested arches. To a TFPL is assigned a triple $(u,v;w)$ of…
It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a x b x c. In this note, this result is proved by constructing…
In this article, we are interested in the enumeration of Fully Packed Loops configurations on a grid with a given noncrossing matching. These quantities also appear as the groundstate components of the Completely Packed Loops model as…
We present new conjectures on the distribution of link patterns for fully-packed loop (FPL) configurations that are invariant, or almost invariant, under a quarter turn rotation, extending previous conjectures of Razumov and Stroganov and…
New conjectures are proposed on the numbers of FPL configurations pertaining to certain types of link patterns. Making use of the Razumov and Stroganov Ansatz, these conjectures are based on the analysis of the ground state of the…
In this work we continue our study of Fully Packed Loop (FPL) configurations in a triangle. These are certain subgraphs on a triangular subset of the square lattice, which first arose in the study of the usual FPL configurations on a square…
We describe a new conjecture involving Fully Packed Loop counting which relates recent observations of Thapper to formulae in the Temperley--Lieb model of loops, and how it implies the Razumov--Stroganov conjecture.
Triangular fully packed loop configurations (TFPLs) emerged as auxiliary objects in the study of fully packed loop configurations on a square (FPLs) corresponding to link patterns with a large number of nested arches. Wieland gyration, on…
The Fully-Packed Loop (FPL) model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin in 1991. Using the two-component Coulomb-Gas approach of Kondev, de…
Distinctive power of the alliance polynomial has been studied in previous works, for instance, it has been proved that the empty, path, cycle, complete, complete without one edge and star graphs are characterized by its alliance polynomial.…
Motivated by Chudnovsky's structure theorem of bull-free graphs, Abu-Khzam, Feghali, and M\"uller have recently proved that deciding if a graph has a vertex partition into disjoint cliques and a triangle-free graph is NP-complete for five…
We discuss a conjecture concerning the enumeration of nonsingular matrices over a finite field that are block companion and whose order is the maximum possible in the corresponding general linear group. A special case is proved using some…
In this work, we put to light a formula that relies the number of fully packed loop configurations (FPLs) associated to a given coupling pi to the number of half-turn symmetric FPLs (HTFPLs) of even size whose coupling is a punctured…
Suppose that $\langle f_n \rangle$ is a sequence of polynomials, $\langle f_n^{(k)}(0)\rangle$ converges for every non-negative integer $k$, and that the limit is not $0$ for some $k$. It is shown that if all the zeros of $f_1, f_2, \dots$…