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Enumeration of alternating sign matrices of even size (quasi)-invariant under a quarter-turn rotation
[article]

2009
*
arXiv
*
pre-print

The aim

arXiv:0906.3445v1
fatcat:dhvyc5jw4nc65jpqbixx6eyige
*of*this work is to*enumerate**alternating**sign**matrices*(ASM) that are*quasi*-*invariant**under**a**quarter*-*turn*. ... The*enumeration*formula (conjectured by Duchon) involves, as*a*product*of*three terms, the number*of*unrestricted ASM's and the number*of*half-*turn*symmetric ASM's. ... Fig. 4 : 4 Partition functions for (q)QTASM*of**even**size*Lemma 8 [ 8 Yang-Baxter equation] If xyz =*a*, We multiply the left-hand side by σ(az), with z = axy. ...##
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Enumeration of Alternating Sign Matrices of Even Size (Quasi-)Invariant under a Quarter-Turn Rotation

2010
*
Electronic Journal of Combinatorics
*

The aim

doi:10.37236/323
fatcat:lgzm6m4rhvhu5d7sphi2ilmjce
*of*this work is to*enumerate**alternating**sign**matrices*(ASM) that are*quasi*-*invariant**under**a**quarter*-*turn*. ... The*enumeration*formula (conjectured by Duchon) involves, as*a*product*of*three terms, the number*of*unrestricted ASM's and the number*of*half-*turn*symmetric ASM's. ... ASM's*quasi*-*invariant**under**a**quarter*-*turn*The class*of*ASM's*invariant**under**a**rotation*by*a**quarter*-*turn*(QTASM) is non-empty in*size*4N − 1, 4N , and 4N + 1. ...##
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Enumeration of alternating sign matrices of even size (quasi)-invariant under a quarter-turn rotation

2009
*
Discrete Mathematics & Theoretical Computer Science
*

International audience The aim

doi:10.46298/dmtcs.2726
fatcat:3p6ufke2ojc5tlswbktmvzr7ku
*of*this work is to*enumerate**alternating**sign**matrices*(ASM) that are*quasi*-*invariant**under**a**quarter*-*turn*. ... L'objet de ce travail est d'énumérer les*matrices**à**signes**alternants*(ASM)*quasi*-*invariantes*par*rotation*d'un quart-de-tour. ... . , x 2N , x, y)*Enumeration**of**alternating**sign**matrices**of**even**size*(*quasi*)-*invariant**under**a**quarter*-*turn**rotation*119 Theorem 6 When*a*= ω 6 = exp(iπ/3), one has for N ≥ 1: Z QT (4N ; X 2N −1 , ...##
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Enumeration of alternating sign matrices of even size (quasi-)nvariant under a quarter-turn rotation
[article]

2009
*
arXiv
*
pre-print

The aim

arXiv:0910.3047v1
fatcat:hf6lgj6xbjdsvczeptq2wmqdvu
*of*this work is to*enumerate**alternating**sign**matrices*(ASM) that are*quasi*-*invariant**under**a**quarter*-*turn*. ... The*enumeration*formula (conjectured by Duchon) involves, as*a*product*of*three terms, the number*of*unrestricted ASM's and the number*of*half-*turn*symmetric ASM's. ... ASM's*quasi*-*invariant**under**a**quarter*-*turn*The class*of*ASM's*invariant**under**a**rotation*by*a**quarter*-*turn*(QTASM) is non-empty in*size*4N − 1, 4N , and 4N + 1. ...##
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Enumeration of alternating sign matrices of even size (quasi-)invariant under a quarter-turn rotation

2010
unpublished

The aim

fatcat:5z7piofnqjho7pebnql3zq2imm
*of*this work is to*enumerate**alternating**sign**matrices*(ASM) that are*quasi*-*invariant**under**a**quarter*-*turn*. ... The*enumeration*formula (conjectured by Duchon) involves, as*a*product*of*three terms, the number*of*unrestricted ASM's and the number*of*half-*turn*symmetric ASM's. ... ASM's*quasi*-*invariant**under**a**quarter*-*turn*The class*of*ASM's*invariant**under**a**rotation*by*a**quarter*-*turn*(QTASM) is non-empty in*size*4N − 1, 4N, and 4N + 1. ...##
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On the link pattern distribution of quarter-turn symmetric FPL configurations

2008
*
Discrete Mathematics & Theoretical Computer Science
*

International audience We present new conjectures on the distribution

doi:10.46298/dmtcs.3644
fatcat:xqqf7ncfdzgypksk57bxkihote
*of*link patterns for fully-packed loop (FPL) configurations that are*invariant*, or almost*invariant*,*under**a**quarter**turn**rotation*, ... As*a*byproduct, we get*a*formula for the*enumeration**of**a*new class*of**quasi*-symmetry*of*plane partitions. ... comments on*a*previous version*of*this paper. ...##
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On the link pattern distribution of quarter-turn symmetric FPL configurations
[article]

2007
*
arXiv
*
pre-print

We present new conjectures on the distribution

arXiv:0711.2871v1
fatcat:eh4mj7dg6fatnckvqjfaffbvw4
*of*link patterns for fully-packed loop (FPL) configurations that are*invariant*, or almost*invariant*,*under**a**quarter**turn**rotation*, extending previous conjectures ... As*a*byproduct, we get*a*formula for the*enumeration**of**a*new class*of**quasi*-symmetry*of*plane partitions. ... QTFPLs*of**even**size*N only exist if N is*a*multiple*of*4, which is easiest seen on the corresponding*alternating*-*sign**matrices*: the sum*of*entries in any*quarter**of*the square has to be exactly*a**quarter*...##
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Enumeration of Perfect Matchings in Graphs with Reflective Symmetry

1997
*
Journal of combinatorial theory. Series A
*

Finally, we consider symmetry classes

doi:10.1006/jcta.1996.2725
fatcat:cn7fwlspszfxzix6xlokzolape
*of*perfect matchings*of*the Aztec diamond graph and we solve the previously open problem*of**enumerating*the matchings that are*invariant**under**a**rotation*by 90 degrees ...*A*plane graph is called symmetric if it is*invariant**under*the re ection across some straight line. ... I would also like to thank the referee for the careful reading*of*the manuscript. ...##
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Twenty-Vertex Model with Domain Wall Boundaries and Domino Tilings

2020
*
Electronic Journal of Combinatorics
*

The four

doi:10.37236/8809
fatcat:wvfqewhg6jgwdftashar4aklmu
*enumeration*problems are reformulated in terms*of*four types*of**Alternating*Phase*Matrices*with entries $0$ and sixth roots*of*unity, subject to suitable*alternation*conditions. ... In types 1 and 2, the configurations are shown to be equinumerous to the*quarter*-*turn*symmetric domino tilings*of*an Aztec-like holey square, with*a*central cross-shaped hole. ... We wish to*enumerate*the domino tilings*of*this domain that are*invariant**under**a**quarter*-*turn**rotation*(i.e.*of*angle π/2) around the center*of*the cross. ...##
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A one-parameter refinement of the Razumov-Stroganov correspondence
[article]

2012
*
arXiv
*
pre-print

We introduce and prove

arXiv:1202.5253v1
fatcat:5esyt3huczgjhpsmjkt53vtieq
*a*one-parameter refinement*of*the Razumov-Stroganov correspondence. ... We show that the*enumeration*vector associated to such FPLs, weighted according to the position*of*the straight line and refined according to the link pattern for the black boundary points, is the ground ... This family*of*domains includes some*of*the "symmetry classes"*of*FPL (or equivalently*of**Alternating**Sign**Matrices*) for which*a*Razumov-Stroganov conjecture was formulated, namely HTASM and QTASM (half-*turn*...##
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Diagonally and antidiagonally symmetric alternating sign matrices of odd order

2017
*
Advances in Mathematics
*

We study the

doi:10.1016/j.aim.2017.05.014
fatcat:xaifnp47nfcjjlmbjc76kebxoi
*enumeration**of*diagonally and antidiagonally symmetric*alternating**sign**matrices*(DASASMs)*of*fixed odd order by introducing*a*case*of*the six-vertex model whose configurations are in bijection ... Among the several product formulae for the*enumeration**of*symmetric*alternating**sign**matrices*which were conjectured in the 1980's, that for odd-order DASASMs is the last to have been proved. ... The third author acknowledges support from Research Programs L1-069 and Z1-5434*of*the Slovenian Research Agency. ...##
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Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order
[article]

2016
*
arXiv
*
pre-print

For each α∈{0,1,-1}, we count

arXiv:1611.03823v1
fatcat:j2xbyfkhk5gwlhhbyvwvuztkza
*alternating**sign**matrices*that are*invariant**under*reflections in the diagonal and in the antidiagonal (DASASMs)*of*fixed odd order with*a*maximal number*of*α's along the ... In these*enumerations*, we encounter product formulas that have previously appeared in plane partition or*alternating**sign*matrix counting, namely for the number*of*all*alternating**sign**matrices*, the number ... order and*quarter*-*turn*symmetric ASMs*of**even*order. ...##
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Arctic Curves of the Six-Vertex Model on Generic Domains: The Tangent Method

2016
*
Journal of statistical physics
*

We adapt the method to work for

doi:10.1007/s10955-016-1590-0
fatcat:43lwglgxqrdwdf6rxrgwp73khy
*a*large class*of*domains, and for other models exhibiting limit shape phenomena. ... We study in detail some examples, and derive, in particular, the Arctic curve*of*the six-vertex model in*a*triangoloid domain at the ice-point. ...*Alternating**Sign**Matrices*An*Alternating**Sign*Matrix (ASM)*of**size*n is an n × n matrix valued in {0, ±1}, such that: (i) non-zero entries*alternate*in*sign*along rows and columns; (ii) the sum*of*entries ...##
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Arctic curves of the twenty-vertex model with domain wall boundaries
[article]

2019
*
arXiv
*
pre-print

We finally compute the arctic curve

arXiv:1910.06833v1
fatcat:kf3pvsbb4nbathwae4si52orve
*of*the*Quarter*-*turn*symmetric Holey Aztec Domino Tiling (QTHADT) model,*a*problem closely related to the 20V model and whose asymptotics may be analyzed via*a*similar ... The latter displays*a*large variety*of*shapes depending on the weights and separates*a*central liquid phase from up to six different frozen phases. ... -Vlaanderen (FWO)*under*EOS project no 30889451. ...##
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Remarks on the construction and the ergodicity properties of dual unitary quantum circuits (with an Appendix by Roland Bacher and Denis Serre)
[article]

2022
*
arXiv
*
pre-print

They appear locally as the most chaotic and most scrambling circuits, nevertheless they can show global

arXiv:2201.07768v2
fatcat:y5sksklb6zaftk5bobjuipzzxa
*signs**of*non-ergodicity: if the perfect tensor is constructed from*a*linear map over finite fields ... Afterwards we consider the ergodicity properties*of**a*special class*of*dual unitary models, where the local gate is*a*permutation matrix. ...*Alternatively*, for an*even*number*of*legs they can be seen as multi-unitary operators for every bi-partitioning*of*the legs into two subsets with equal*size*[20] . ...
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