A combustion system (100; 500), comprising: - a fuel and oxidant source (101; 601) configured to output fuel and oxidant; and - a flame holder (102; 402; 502; 602; 702; 802; 902; 1002) positioned to receive the fuel and oxidant, the flame holder (102; 402; 502; 602; 702; 802; 902; 1002) including: - an array of elongate members arranged in parallel with each other and defining a plurality of combustion channels (210; 708; 808; 908; 1008) between adjacent elongate members, a width of each combustion channel being a distance between adjacent elongate members, a height of each combustion channel corresponding to a height of the elongate members on an axis corresponding to a general direction of output of the fuel and oxidant from the fuel and oxidant source (101; 601), the height being at least five times the width, the flame holder (102; 402; 502; 602; 702; 802; 902; 1002) being configured to sustain a combustion reaction of the fuel and oxidant within the combustion channels (210; 708; 808; 908; 1008); and - a support structure (106; 406; 506; 606) holding the array of elongate members, characterized in that said elongate members are a plurality of discrete slats (104; 404; 505; 604; 904; 1004) held in parallel with each other in slots defined by support arms of the support structure; wherein each slat comprises: - a first edge proximal to the fuel and oxidant source (101; 601); and - a second edge distal from the fuel and oxidant source (101; 601); and wherein the width of each combustion channel corresponds to a distance between the respective adjacent slats (104; 404; 505; 604; 904; 1004) and the length of each combustion channel corresponds to a distance between the first edge and the second edge of one of the respective adjacent slats (104; 404; 505; 604; 904; 1004). - a fuel and oxidant source (101; 601) configured to output fuel and oxidant; and - a flame holder (102; 402; 502; 602; 702; 802; 902; 1002) positioned to receive the fuel and oxidant, the flame holder (102; 402; 502; 602; 702; 802; 902; 1002) including: - an array of elongate members arranged in parallel with each other and defining a plurality of combustion channels (210; 708; 808; 908; 1008) between adjacent elongate members, a width of each combustion channel being a distance between adjacent elongate members, a height of each combustion channel corresponding to a height of the elongate members on an axis corresponding to a general direction of output of the fuel and oxidant from the fuel and oxidant source (101; 601), the height being at least five times the width, the flame holder (102; 402; 502; 602; 702; 802; 902; 1002) being configured to sustain a combustion reaction of the fuel and oxidant within the combustion channels (210; 708; 808; 908; 1008); and - a support structure (106; 406; 506; 606) holding the array of elongate members, - an array of elongate members arranged in parallel with each other and defining a plurality of combustion channels (210; 708; 808; 908; 1008) between adjacent elongate members, a width of each combustion channel being a distance between adjacent elongate members, a height of each combustion channel corresponding to a height of the elongate members on an axis corresponding to a general direction of output of the fuel and oxidant from the fuel and oxidant source (101; 601), the height being at least five times the width, the flame holder (102; 402; 502; 602; 702; 802; 902; 1002) being configured to sustain a combustion reaction of the fuel and oxidant within the combustion channels (210; 708; 808; 908; 1008); and - a support structure (106; 406; 506; 606) holding the array of elongate members, said elongate members are a plurality of discrete slats (104; 404; 505; 604; 904; 1004) held in parallel with each other in slots defined by support arms of the support structure; wherein each slat comprises: - a first edge proximal to the fuel and oxidant source (101; 601); and - a second edge distal from the fuel and oxidant source (101; 601); and - a first edge proximal to the fuel and oxidant source (101; 601); and - a second edge distal from the fuel and oxidant source (101; 601); and wherein the width of each combustion channel corresponds to a distance between the respective adjacent slats (104; 404; 505; 604; 904; 1004) and the length of each combustion channel corresponds to a distance between the first edge and the second edge of one of the respective adjacent slats (104; 404; 505; 604; 904; 1004).