


default search action
The Electronic Journal of Combinatorics, Volume 30
Volume 30, Number 1, 2023
- Nicholas J. Williams
:
The First Higher Stasheff-Tamari Orders are Quotients of the Higher Bruhat Orders. - Irina Ðankovic, Maria-Romina Ivan
:
Saturation for Small Antichains. - James G. Oxley, Jagdeep Singh:
Generalizing Cographs to 2-Cographs. - Azzurra Ciliberti
, Luca Moci:
On Chromatic Symmetric Homology and Planarity of Graphs. - Adam Gregory, Zachary Hamaker
:
Lenart's Bijection via Bumpless Pipe Dreams. - R. Amzi Jeffs:
Decompositions of Augmented Bergman Complexes. - Eoghan McDowell:
Flagged Schur Polynomial Duality via a Lattice Path Bijection. - Bishal Deb
:
Bijection Between Increasing Binary Trees and Rook Placements on Double Staircases. - Claire Hilaire, Jean-Florent Raymond:
Long Induced Paths in Minor-Closed Graph Classes and Beyond. - Alan M. Frieze, Wesley Pegden
:
Multitrees in Random Graphs. - Giuseppe Cotardo, Alberto Ravagnani:
Rank-Metric Lattices. - Brendan Pawlowski, Eric Ramos, Brendon Rhoades:
Spanning Configurations and Representation Stability. - Deepak Bal
, Patrick Bennett
:
The Matching Process and Independent Process in Random Regular Graphs and Hypergraphs. - David Ellis
, Imre Leader, Maria-Romina Ivan
:
Small Sets in Union-Closed Families. - David Iglesias, Eduardo Lucas:
On a Characterization of Lattice Cubes via Discrete Isoperimetric Inequalities. - Andries E. Brouwer:
The Equivalence of Two Inequalities for Quasisymmetric Designs. - Sergey Kitaev
, Artem V. Pyatkin:
On Permutations Avoiding Partially Ordered Patterns Defined by Bipartite Graphs. - Allan Lo, Vincent Pfenninger:
Towards Lehel's Conjecture for 4-Uniform Tight Cycles. - Yun Cheng, Yixue Liu, Tomasz Tkocz, Albert Xu:
Typical Values of Extremal-Weight Combinatorial Structures with Independent Symmetric Weights. - Baptiste Louf, Fiona Skerman:
Finding Large Expanders in Graphs: from Topological Minors to Induced Subgraphs. - Zachary Hunter:
A Result on Large Induced Subgraphs with Prescribed Residues in Bipartite Graphs. - Radoslav Fulek, Michael J. Pelsmajer, Marcus Schaefer
:
Hanani-Tutte for Radial Planarity II. - Peter Bradshaw:
Cooperative Colorings of Forests. - George Spahn:
Counting Baxter Matrices. - Izhak Elmaleh, Ohad N. Feldheim:
Min-Cost-Flow Preserving Bijection Between Subgraphs and Orientations. - Jan De Beule
, Jozefien D'haeseleer, Ferdinand Ihringer, Jonathan Mannaert
:
Degree 2 Boolean Functions on Grassmann Graphs. - Tomoo Matsumura:
A Tableau Formula for Vexillary Schubert Polynomials in Type C. - Vladislav V. Kabanov:
A New Construction of Strongly Regular Graphs with Parameters of the Complement Symplectic Graph. - Clemens Heuberger, Sarah J. Selkirk
, Stephan G. Wagner:
Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo $k$. - Ajani De Vas Gunasekara, Daniel Horsley
:
Smaller Embeddings of Partial $k$-Star Decompositions. - Zhenyu Ni, Jing Wang, Liying Kang:
Spectral Extremal Graphs for Disjoint Cliques. - Stéphane Bessy, Johannes Pardey, Lucas Picasarri-Arrieta, Dieter Rautenbach:
Unbalanced Spanning Subgraphs in Edge Labeled Complete Graphs. - Criel Merino:
The Number of Quasi-Trees in Fans and Wheels. - Felix Bock, Rafal Kalinowski
, Johannes Pardey, Monika Pilsniak
, Dieter Rautenbach, Mariusz Wozniak
:
Majority Edge-Colorings of Graphs. - Manoel Lemos, James G. Oxley:
An Upper Bound for the Circumference of a 3-Connected Binary Matroid. - Isaac Konan:
A Bijective Proof of a Generalization of the Non-Negative Crank-Odd Mex Identity. - Sean Eberhard
, Freddie Manners
:
The Apparent Structure of Dense Sidon Sets. - Dániel Gerbner:
Generalized Turán problems for $K_{2,t}$. - Bennet Goeckner, Fran Herr, Legrand Jones, Rowan Rowlands:
A Characterization of Two-Dimensional Buchsbaum Matching Complexes. - James A. Long Jr., Kevin G. Milans, Andrea Munaro
:
Non-Empty Intersection of Longest Paths in $H$-Free Graphs. - Wei Wang, Wei Wang, Tao Yue:
Graphs with at most one Generalized Cospectral Mate. - Binlong Li, Bo Ning
:
Stability of Woodall's Theorem and Spectral Conditions for Large Cycles. - Jonathan Jedwab, Shuxing Li, Samuel Simon:
Constructions and Restrictions for Balanced Splittable Hadamard Matrices. - Kevin Zhao:
On Davenport Constant of the Group $C_2^{r-1} \oplus C_{2k}$. - Sergey V. Avgustinovich, Sergey Kitaev
, Anna A. Taranenko:
On Five Types of Crucial Permutations with Respect to Monotone Patterns. - Zuwen Luo, Kexiang Xu
:
On the Local and Global Mean Orders of Sub-$k$-Trees of $k$-Trees. - Sylwia Antoniuk, Nina Kamcev
, Andrzej Rucinski
:
Properly Colored Hamilton Cycles in Dirac-Type Hypergraphs. - Maya Stein:
Monochromatic Paths in 2-Edge-Coloured Graphs and Hypergraphs. - Yuval Filmus:
Junta Threshold for Low Degree Boolean Functions on the Slice. - Antoine Domenech, Pascal Ochem:
Doubled Patterns with Reversal and Square-Free Doubled Patterns. - Sandip Das, Sumitava Ghosh, Swathy Prabhu, Sagnik Sen:
A Homomorphic Polynomial for Oriented Graphs. - Antoine Dailly, Laura Eslava
, Adriana Hansberg, Denae Ventura:
The Balancing Number and Generalized Balancing Number of Some Graph Classes. - Freddie Illingworth
, Emil Powierski, Alex D. Scott, Youri Tamitegama:
Balancing Connected Colourings of Graphs. - Hyunsoo Cho, JiSun Huh, Hayan Nam, Jaebum Sohn:
Combinatorics on Bounded Free Motzkin Paths and its Applications. - Grahame Erskine
, James Tuite
:
Small Graphs and Hypergraphs of Given Degree and Girth. - Andrzej Grzesik, Ervin Györi, Nika Salia
, Casey Tompkins:
Subgraph Densities in $K_r$-Free Graphs. - Nacho López
, Arnau Messegué
, Josep M. Miret:
Nonexistence of Almost Moore Digraphs of Degrees 4 and 5 with Self-Repeats.
Volume 30, Number 2, 2023
- Federico Romaniello, Jean Paul Zerafa:
Betwixt and Between 2-Factor Hamiltonian and Perfect-Matching-Hamiltonian Graphs. - Manoj Kummini, Dharm Veer:
The $h$-Polynomial and the Rook Polynomial of some Polyominoes. - Ragnar Freij-Hollanti, Relinde Jurrius
, Olga Kuznetsova:
Combinatorial Derived Matroids. - Alin Bostan, Sergey Yurkevich:
On the $q$-Analogue of Pólya's Theorem. - Zheng-Jiang Xia, Jae-Ho Lee
, Jack H. Koolen:
A New Feasibility Condition for the AT4 Family. - Wei Li, Yao Wang:
Enumeration of Perfect Matchings of the Cartesian Products of Graphs. - Denis S. Krotov:
Perfect Colorings of the Infinite Square Grid: Coverings and Twin Colors. - Marek Sokolowski:
Bounds on Half Graph Orders in Powers of Sparse Graphs. - Han Wang, Zhi-Wei Sun:
Proof of a Conjecture Involving Derangements and Roots of Unity. - Tom Johnston
:
Zero-Sum Squares in $\{-1, 1\}$-Matrices with Low Discrepancy. - Pawel Gawrychowski, Tomasz Kociumaka, Wojciech Rytter, Tomasz Walen:
Tight Bound for the Number of Distinct Palindromes in a Tree. - Michael Anastos:
A Note on Long Cycles in Sparse Random Graphs. - Gregg Musiker, Kayla Wright:
Mixed Dimer Configuration Model in Type D Cluster Algebras. - José L. Fernández, Pablo Fernández
:
Some Arithmetic Properties of Pólya's Urn. - Claudio Alexandre Piedade
:
Infinite Families of Hypertopes from Centrally Symmetric Polytopes. - Faqruddin Ali Azam, Edward Richmond
:
On the Generating Function for Intervals in Young's Lattice. - Yinsong Chen, Vladislav Kargin:
On Enumeration and Entropy of Ribbon Tilings. - Zhenzhen Lou, Mingfei Gao, Qiongxiang Huang:
On the Spectral Radius of Minimally 2-(Edge)-Connected Graphs with Given Size. - Dandan Fan, Xueyi Huang, Huiqiu Lin:
Spectral Radius Conditions for the Rigidity of Graphs. - Éric Fusy, Erkan Narmanli, Gilles Schaeffer:
Enumeration of Corner Polyhedra and 3-Connected Schnyder Labelings. - Patrick Arras:
Ore- and Pósa-Type Conditions for Partitioning 2-Edge-Coloured Graphs into Monochromatic Cycles. - Nándor Sieben:
Impartial Hypergraph Games. - George Drummond
, Charles Semple
:
A Splitter Theorem for Elastic Elements in 3-Connected Matroids. - Chunqiu Fang, Ervin Györi, Chuanqi Xiao, Jimeng Xiao:
Turán Numbers and Anti-Ramsey Numbers for Short Cycles in Complete $3$-Partite Graphs. - Liam Armstrong, Bryan Ducasse, Thomas Meyer, Holly Swisher:
Generalized Alder-Type Partition Inequalities. - Kagan Kursungöz, Halime Ömrüuzun Seyrek:
Combinatorial Constructions of Generating Functions of Cylindric Partitions with Small Profiles into Unrestricted or Distinct Parts. - Tolson Bell:
The Park-Pham Theorem with Optimal Convergence Rate. - Davoud Abdi:
A Cantor-Bendixson Rank for Siblings of Trees. - Svante Janson, Valentas Kurauskas:
Estimating Global Subgraph Counts by Sampling. - Nicolas Folinsbee, Joel Friedman
:
Generalized Riemann Functions, Their Weights, and the Complete Graph. - Antonino Ficarra
, Jürgen Herzog, Takayuki Hibi:
Behaviour of the Normalized Depth Function. - Kevin Liu
:
Characterizing Planar Tanglegram Layouts and Applications to Edge Insertion Problems. - Robert Hickingbotham
:
Induced Subgraphs and Path Decompositions. - Dariusz Dereniowski, Przemyslaw Gordinowicz, Pawel Pralat:
Edge and Pair Queries-Random Graphs and Complexity. - Luiz Emilio Allem
, Elismar R. Oliveira
, Fernando Tura:
Generating $I$-Eigenvalue Free Threshold Graphs. - Svante Janson:
The Number of Occurrences of Patterns in a Random Tree or Forest Permutation. - Cheolwon Heo
, Hyobin Kim, Mark H. Siggers:
The Complexity of the Matroid Homomorphism Problem. - João Paulo Costalonga, Talmage James Reid, Haidong Wu:
Rooted Prism-Minors and Disjoint Cycles Containing a Specified Edge. - Pavel Shuldiner, R. Wayne Oldford:
How Many Cliques Can a Clique Cover Cover? - Jonathan A. Noel
, Arjun Ranganathan:
On the Running Time of Hypergraph Bootstrap Percolation. - Jane Ivy Coons, Seth Sullivant
:
The $h^*$-Polynomial of the Order Polytope of the Zig-Zag Poset. - Zhipeng Lu
:
On Counting Double Centralizers of Symmetric Groups. - Michael Krul, Lubos Thoma:
An Algebraic Formulation of Hypergraph Colorings. - Bojan Basic, Aleksa Dzuklevski, Anna Slivková
:
Solutions to Seven and a Half Problems on Tilings. - Tara Abrishami, Maria Chudnovsky
, Sepehr Hajebi, Sophie Spirkl:
Induced Subgraphs and Tree Decompositions IV. (Even Hole, Diamond, Pyramid)-Free Graphs. - Tara Gomes, Christopher O'Neill, Eduardo Torres Davila:
Numerical Semigroups, Polyhedra, and Posets III: Minimal Presentations and Face Dimension. - Aram Dermenjian
:
Maximal Degree Subposets of $\nu$-Tamari Lattices. - Vsevolod F. Lev, Oriol Serra:
Towards $3n-4$ in groups of prime order. - Ron M. Adin
, Yuval Roichman:
Cyclic Descents, Matchings and Schur-Positivity. - Alheydis Geiger
, Marta Panizzut:
A Tropical Count of Real Bitangents to Plane Quartic Curves. - Sami Assaf, Danjoseph Quijada:
Monk's Rule for Demazure Characters of the General Linear Group. - Mark Holmes, Alexander E. Holroyd, Alejandro Ramírez:
Cyclic Products and Optimal Traps in Cyclic Birth and Death Chains. - Michael Drmota, Marc Noy, Clément Requilé
, Juanjo Rué:
Random Cubic Planar Maps. - Mikhail Isaev, Mihyun Kang
:
On the Chromatic Number in the Stochastic Block Model. - Lyuben Lichev, Dieter Mitsche:
On the Minimum Bisection of Random 3-Regular Graphs. - Margaret Bayer, Marija Jelic Milutinovic
, Julianne Vega:
Perfect Matching Complexes of Honeycomb Graphs. - Hadi Kharaghani, Sho Suda:
Hadamard Matrices related to Projective Planes.
Volume 30, Number 3, 2023
- Irfan Durmic, Alex Han, Pamela E. Harris
, Rodrigo Ribeiro, Mei Yin:
Probabilistic Parking Functions. - Susan Jowett, Jasmine Lulani Kaulamatoa, Geoff Whittle:
Bounding Branch-Width. - Yair Caro, Adriana Hansberg, Amanda Montejano
:
Graphs Isomorphisms Under Edge-Replacements and the Family of Amoebas. - Florent Foucaud, Tuomo Lehtilä
:
Bounds and Extremal Graphs for Total Dominating Identifying Codes. - Nicolas Bousquet, Bastien Durain, Théo Pierron, Stéphan Thomassé:
Extremal Independent Set Reconfiguration. - Ben Adenbaum
, Sergi Elizalde
:
Rowmotion on 321-Avoiding Permutations. - David Callan, Vít Jelínek, Toufik Mansour:
Inversion Sequences Avoiding a Triple of Patterns of 3 Letters. - Ferenc Bencs, Jeroen Huijben, Guus Regts:
On the Location of Chromatic Zeros of Series-Parallel Graphs. - Daoji Huang:
Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams. - Qing Zeng, Yuefeng Yang, Kaishun Wang:
P-Polynomial Weakly Distance-Regular Digraphs. - Johannes Carmesin, Tsvetomir Mihaylov:
Outerspatial 2-Complexes: Extending the Class of Outerplanar Graphs to Three Dimensions. - Siddharth Berera, Andrés Gómez-Colunga, Joey Lakerdas-Gayle, John López, Mauditra Matin, Daniel Roebuck, Eric Rowland, Noam Scully, Juliet Whidden:
The Lexicographically Least Square-Free Word with a Given Prefix. - Tuan A. Do, Joshua Erde, Mihyun Kang
, Michael Missethan:
Component Behaviour and Excess of Random Bipartite Graphs Near the Critical Point. - Rutger Campbell, Marc Distel, J. Pascal Gollin
, Daniel J. Harvey, Kevin Hendrey, Robert Hickingbotham
, Bojan Mohar, David R. Wood:
Graphs of Linear Growth have Bounded Treewidth. - Michael Anastos, David Fabian, Alp Müyesser, Tibor Szabó:
Splitting Matchings and the Ryser-Brualdi-Stein Conjecture for Multisets. - Felix Christian Clemen, Adam Zsolt Wagner:
Balanced Edge-Colorings Avoiding Rainbow Cliques of Size Four. - Tung Nguyen:
A Further Extension of Rödl's Theorem. - Chunlin You, Qizhong Lin:
Ramsey Numbers of Large Even Cycles and Fans. - Andrea Lucchini
, Pablo Spiga:
Hypermaps Over Non-Abelian Simple Groups and Strongly Symmetric Generating Sets. - Sebastian M. Cioaba, Sean Dewar
, Georg Grasegger
, Xiaofeng Gu:
Graph Rigidity Properties of Ramanujan Graphs. - Sebastian König:
Combinatorics of Centers of 0-Hecke Algebras in Type A. - Daryl Funk, Dillon Mayhew, Mike Newman:
Tree Automata and Pigeonhole Classes of Matroids: II. - Jesse Kim, James Propp:
A Pentagonal Number Theorem for Tribone Tilings. - Filippo Disanto, Michael Fuchs
:
Distribution of External Branch Lengths in Yule Histories. - Kevin Woods:
The Generalized Frobenius Problem via Restricted Partition Functions. - Oleg Pikhurko:
On the Limit of the Positive $\ell$-Degree Turán Problem. - Ethan Pesikoff, Benjamin Przybocki
, Janabel Xia:
The Maximum Hook Length of $d$-Distinct Simultaneous Core Partitions. - Yuval Filmus, Edward A. Hirsch, Sascha Kurz, Ferdinand Ihringer, Artur Ryazanov, Alexander V. Smal, Marc Vinyals:
Irreducible Subcube Partitions. - Matías Pavez-Signé, Simón Piga, Nicolás Sanhueza-Matamala
:
Ramsey Numbers with Prescribed Rate of Growth. - Eve Vidalis:
A Combinatorial Proof of Buryak-Feigin-Nakajima. - Jesper Nederlof, Michal Pilipczuk, Karol Wegrzycki
:
Bounding Generalized Coloring Numbers of Planar Graphs Using Coin Models. - Ludivine Leclere, Sophie Morier-Genoud:
Quantum Continuants, Quantum Rotundus and Triangulations of Annuli. - Ming-Zhu Chen, Shuchao Li, Zhao-Ming Li, Yuantian Yu, Xiao-Dong Zhang:
An Aα-Spectral Erdős-Sós Theorem. - Linda Cook, Tomás Masarík, Marcin Pilipczuk, Amadeus Reinald, Uéverton S. Souza:
Proving a Directed Analogue of the Gyárfás-Sumner Conjecture for Orientations of $P_4$. - Florent Foucaud, Reza Naserasr, Rongxing Xu:
Extended Double Covers and Homomorphism Bounds of Signed Graphs. - Michael Drmota, Marc Noy, Benedikt Stufler:
Cut Vertices in Random Planar Maps.
Volume 30, Number 4, 2023
- Beka Ergemlidze, Ervin Györi, Abhishek Methuku, Nika Salia
, Casey Tompkins:
On $3$-uniform hypergraphs avoiding a cycle of length four. - Paul Bastide, Marthe Bonamy, Anthony Bonato, Pierre Charbit, Shahin Kamali, Théo Pierron, Mikaël Rabie:
Improved Pyrotechnics: Closer to the Burning Number Conjecture. - David Ellis
, Dylan King:
Lower Bounds for the Turán Densities of Daisies. - Anders Claesson, Atli Fannar Franklín, Einar Steingrímsson:
Permutations with Few Inversions. - Hsien-Kuei Hwang
:
A Curious Identity Arising From Stirling's Formula and Saddle-Point Method on Two Different Contours. - Michael Savery:
Planar Graphs with the Maximum Number of Induced 6-Cycles. - Josse van Dobben de Bruyn, Dion Gijswijt
:
On the Size of Subsets of $\mathbb{F}_q^n$ Avoiding Solutions to Linear Systems with Repeated Columns. - Mikhail Goltsblat
:
Ninth Variation of Classical Group Characters of Type A-D and Littlewood Identities. - Yi-Lin Lee:
Off-Diagonally Symmetric Domino Tilings of the Aztec Diamond. - Yasuaki Gyoda
, Kodai Matsushita:
Generalization of Markov Diophantine Equation via Generalized Cluster Algebra. - Ming Han, Tao Wang
, Jianglin Wu, Huan Zhou, Xuding Zhu:
Weak Degeneracy of Planar Graphs and Locally Planar Graphs. - Dieter Rautenbach, Florian Werner:
Irregularity of Graphs Respecting Degree Bounds. - Peter Bradshaw:
Separating the Online and Offline DP-Chromatic Numbers. - Jorn G. van der Pol:
Almost Every Matroid has an $M(K_4)$- or a $\mathcal{W}^3$-Minor. - Michaela Hiller:
Counterexamples to the Characterisation of Graphs with Equal Independence and Annihilation Number. - Xiangneng Zeng, Pingzhi Yuan:
On Sequences Without Short Zero-Sum Subsequences. - Ming Han, Xuding Zhu:
Weak (2,3)-Decomposition of Planar Graphs. - Georg Loho
, Ben Smith
:
Face Posets of Tropical Polyhedra and Monomial Ideals. - Gwenaël Joret, William Lochet
, Michal T. Seweryn:
Edge Separators for Graphs Excluding a Minor. - Jakub Przybylo
, Fan Wei:
Short Proof of the Asymptotic Confirmation of the Faudree-Lehel Conjecture. - Jianping Pan
, Tianyi Yu:
A Bijection Between K-Kohnert Diagrams and Reverse Set-Valued Tableaux. - Wolfgang Kühnel:
Generalized Heawood Numbers. - Yuxuan Tang, Yue Ma, Xinmin Hou
:
The Degree and Codegree Threshold for Linear Triangle Covering in 3-Graphs. - Igor Araujo, József Balogh, Haoran Luo:
On the Maximum $F_5$-Free Subhypergraphs of a Random Hypergraph. - Lior Gishboliner
, Asaf Shapira:
On Rödl's Theorem for Cographs. - Katherine Tung:
A Bijection Between Evil-Avoiding and Rectangular Permutations. - Sen-Peng Eu, Louis Kao:
Three New Refined Arnold Families. - Kenta Ozeki, Masao Tsugaki:
A Spanning Tree with at Most $k$ Leaves in a $K_{1,p}$-Free Graph. - Julian Matthes:
Finding Large Rainbow Trees in Colourings of $K_{n,n}$. - Péter Pál Pach, Máté Vizer:
Improved Lower Bounds for Multiplicative Square-Free Sequences. - Sayan Goswami, Lorenzo Luperi Baglini, Sourav Kanti Patra:
Polynomial Extension of the Stronger Central Sets Theorem. - Jenya Soprunova
:
Bounds on Area Involving Lattice Size. - Dániel Gerbner:
Some Exact Results for Non-Degenerate Generalized Turán Problems. - Iain Beaton, Danielle Cox, Christopher Duffy
, Nicole Zolkavich:
Chromatic Polynomials of 2-Edge-Coloured Graphs. - Inês Rodrigues
:
An Action of the Cactus Group on Shifted Tableau Crystals. - Vuong Bui
:
The Number of Polyiamonds is Supermultiplicative. - Jan Böker
:
Weisfeiler-Leman Indistinguishability of Graphons. - Niranjan Balachandran, Srimanta Bhattacharya, Krishn Kher, Rogers Mathew, Brahadeesh Sankarnarayanan:
On Hierarchically Closed Fractional Intersecting Families. - Anthony Lazzeroni
:
Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-Commuting Variables. - Pakawut Jiradilok, Thomas McConville:
Roots of Descent Polynomials and an Algebraic Inequality on Hook Lengths. - Emily Gunawan
, Jianping Pan
, Heather M. Russell, Bridget Eileen Tenner:
RSK Tableaux and the Weak Order on Fully Commutative Permutations. - Thomas Hall, Max Kölbl, Koji Matsushita, Sora Miyashita:
Nearly Gorenstein Polytopes. - Andy Fry:
Tropical Moduli Spaces of Rational Graphically Stable Curves. - Fan Zhou:
On Eventually Periodic Sets as Minimal Additive Complements. - Sam Spiro, Erlang Surya, Ji Zeng:
Semi-Restricted Rock, Paper, Scissors.

manage site settings
To protect your privacy, all features that rely on external API calls from your browser are turned off by default. You need to opt-in for them to become active. All settings here will be stored as cookies with your web browser. For more information see our F.A.Q.